OF  THE 
XjNIVERSlTY 

OF       . 

caufor^^ 


TWO  YEARS  WOEK  IN  NUMBERS 


TWO  YEARS  WORK 
IN  NUMBERS 


EXPRESSLY  ARRANGED  FOR  FUNDAMENTAL 

ACQUIREMENT  PRECEDING  THE 

INTERMEDIATE  GRADES 


BY 
MINNIE  ETHEL  PUNTENNEY 

Head  of  Primary  Training  Department  of  Central  State  Normal 

Edmond,  Oklahoma 

Lecturer  in  Teachers'  Institutes  and  Chautauquas 


DOUB  &  COMPANY 
SAN  FRANCISCO 

1908 

All  rights  reserved 


Copyright,    1908 
By  DOUB  &  COMPANY 

SDUCATIOI  LIB3« 

Electrotyped  and  Printed  August,  1908 


PRESS    OF 

LITTLE    &    BECKER    PTG.    CO. 

ST.    LOUIS. 


L  5 1  ^^2) 


PREFACE 


The  purpose  of  this  book  is:  First — ^to  sys- 
tematize the  knowledge  that  the  child  has  when  he 
enters  school;  Second — to  strengthen  and  develop 
his  judgment ;  Third — to  teach  him  to  measure  by 
using  the  simple  units  of  measurement;  Fourth — 
to  lead  him  to  discover,  easily  and  logically,  the 
fundamental  number  facts  of  addition,  subtrac- 
tion, multiplication  and  division;  Fifth — ^to  lead 
him  to  see  the  relation  of  these  number  facts  to  our 
everyday  experience ;  Sixth — to  help  him  to  learn 
these  number  facts  by  pleasing  repetitions;  Sev- 
enth— to  cause  him  to  learn  the  fundamental  pro- 
cesses by  performing  them. 

This  book  contains  the  fundamental  number 
facts  and  processes  required  to  prepare  the  child 
for  the  study  of  any  intermediate  arithmetic.  It 
is  issued  in  two  editions,  the  regular  or  pupil's  edi- 
tion, and  the  teacher's  Manual.  The  two  editions 
are  alike,  except  that  the  teacher's  edition  includes 
pages  ix-xxvi,  which  contain  notes  on  Part  One 
and  Part  Two,  and  an  outline  of  the  work  for  the 
half-year  that   precedes   the   time   at  which   the 


\[  '  Preface 

regular  edition  is  placed  in  the  hands  of  the  pupil. 
The  book  provides  work  for  two  years,  but  during 
the  first  half-year  it  is  not  to  be  in  the  hands  of  the 
pupil.  The  Author  intends  the  work  to  begin  at 
the  beginning  of  the  first-year  grade,  but  the  book 
may  be  used  with  just  as  good  results  in  those 
schools  where  number  work  is  not  begun  until 
the  middle  of  the  first  year  or  the  beginning  of  the 
second. 

For  these  lessons  the  Author  is  indebted  to  the 
manv  hundreds  of  children  and  teachers  whom  it 
has  been  her  pleasure  to  instruct.  She  is  also  very 
grateful  to  all  her  friends  who  have  aided  her  in 
any  way. 

MiNXiE  Ethel  Pu:n^tenney 

Litchfield,  Illinois 
August  15, 1908 


CONTENTS 


Preface    ' v 

Explanatory  and  Suggestive  (in  Teacher's  Edition  only) .    ix 

Introductory    ix 

Sources  of  Material x 

Suggestive  Lessons   xiii 

Notes  on  Part  One xxiii 

Notes  on  Part  Two   xxv 

Part  One 1 

Numbers  One,  Two,  Three,  Four,  Five 3 

The  Number  Three  9 

The  Number  Four   11 

The  Number  Five   19 

The  Number  Six   22 

The  Number  Seven   30 

The  Number  Eight 35 

The  Number  Nine  45 

The  Number  Ten    54 

Part  Two 67 

The  Number  Eleven   69 

The  Number  Twelve 81 

The  Number  Thirteen  92 

The  Number  Fourteen   97 

The  Number  Fifteen 101 

The  Number  Sixteen   107 

The  Number  Seventeen  Ill 

The  Number  Eighteen   116 

The  Number  Nineteen 120 

The  Number  Twenty  . . . 123 

Summary  142 

The  Forty-five  Addition  Combinations 142 

The  Tables  of  Measures 143 

The  Completion  of  Multiplication  Table 145 

The  Numbers  in  Figures,  AA^ords  and  Roman  Numerals  146 

vll 


It  requires  the  patience  of  Job, 
Tine  ^Alisdom  of  Solomon 
And  tine  love  of  God 

To  lead  a  little  child  aright 


rHi 


EXPLANATORY  AND  SUGGESTIVE 


INTRODUCTORY 

.  Each  formal  science  has  a  language.  The  language  of  form 
is  drawing.  The  language  of  harmony  is  music.  The  lan- 
guage of  measurement  is  mathematics.  In  each  of  these 
languages  the  mechanics  requires  much  time.  The  mechanics 
of  mathematics  involves  the  fundamental  number  facts  and 
the  fundamental  processes.  The  mechanics  of  each  language 
must  be  learned ;  therefore,  the  plan  of  this  book  is  to  aid  the 
child  in  learning  the  fundamentals  of  mathematics. 

We  may  ask,  AVhat  is  the  need  of  Mathematics?  Why  was 
a  number  system  formulated?  Simply  because  of  the  limita- 
tation  of  quantity.  If  there  were  an  unlimited  amount  of 
quantity,  no  measurement  would  be  required.  Then  w^e  must 
agree  with  McLellan  and  Dewey  (The  Psychology  of  Number) 
that  the  Number  Idea  has  its  origin  in  measurement.  But 
what  must  we  know  in  order  to  measure?  We  must  have  a 
clear  conception  of  the  unit  of  measure.  We  must  know  the 
process  of  finding  the  ratio  of  one  quantity  used  as  the  unit 
of  measurement  to  another  quantity  to  be  measured. 

For  convenience,  a  number  of  these  facts,  thus  discovered, 
have  been  arranged  in  groups  called  tables.  These  tables 
must  be  learned.  Only  45  addition  facts,  64  multiplication 
facts,  and  double  the  number  of  subtraction  and  division 
facts,  a  few  tables  of  measure,  and  the  fundamental  proc- 
esses with  practical  applications,  make  the  sum  total  of  pri- 
mary number  work. 

When  a  little  child  enters  school,  he  knows  a  great  many 
scattering  facts.  His  experience  has  taught  him  a  few  num- 
ber facts.  He  is  able  to  imagine  and  to  memorize,  but  is 
able  to  do  very  little  reasoning.     His  curiosity  leads  him  to 

ix 


X  Tivo  Years  Work  in  Niimhers 

want  to  discover.  Therefore,  the  principal  work  of  the 
primary  teacher  is  to  lead  the  child  to  discover  and  to  think 
logically.  While  he  is  discovering  and  thinking,  he  will 
necessarily  learn  many  useful  facts. 

The  exercises  throughout  the  book  are  planned  to  lead  the 
child  to  discover  cheerfully,  .to  think  willingly,  to  image  eas- 
ily, to  memorize  readily,  and  to  do  accurately.  All  modern 
psychologists  agree  that  the  motor  activities  intensify  the 
sense  activities,  hence  the  motor  sensations  intensify  the  sense 
images.  If  the  brain  receives  the  sensation  through  the  ear, 
the  eye  and  the  hand,  the  impression  is  much  deeper  than 
the  sensation  received  through  the  ear  only. 


SOURCES  OF  MATERIAL 

In  the  reading  lessons,  both  from  the  board  and  the  book, 
let  the  children  count  the  words  that  are  alike.  This  serves 
a  two-fold  purpose.  The  child  loves  to  count.  Each  time  he 
counts  the  word  he  images  the  word  and  it  soon  becomes  one 
of  his  mental  pictures.  Children  also  love  to  count  the  lines 
in  the  reading  lessons,  the  words  in  the  spelling  columns,  the 
objects  in  the  pictures. 

Let  the  children  count  the  boys  in  the  school  room,  the  girls 
in  the  room,  the  boys  and  girls  in  each  row  of  seats,  the  boys 
and  girls  in  groups,  the  children  at  the  blackboard,  etc. 

A  number  of  counting  lessons  may  be  given  in  connection 
with  the  distribution  of  material,  also  in  connection  with 
plays  and  marches. 

Assist  the  children  in  keeping  a  weather  record.  A  simple 
device  is  a  series  of  circles  drawn  on  the  board.  Designate  the 
portion  of  the  day  that  is  clear,  cloudy  or  stormy.  A  great 
deal  of  number  work  may  be  gotten  from  the  above  device. 
Have  a  thermometer  in  the  room.  Allow  the  children  to 
learn  to  count  from  it. 

Do  not  lose  sight  of  the  number  work  in  Nature  Study  as 
well  as  in  all  observation  work.    In  the  construction  work  use 


Explanatory  and  Suggestive  xi 

such  mathematical  ideas  as  surface,  square,  rectangle,  tri- 
angle, corner,  side  and  edge.  In  the  paper  folding,  teach 
the  right  and  left  side  by  referring  to  the  right  or  left  hand. 
A  great  many  number  computations  are  used  in  connection 
with  the  making  of  things.  Always  take  advantage  of  these 
opportunities  to  teach  practical  number  work.  Make  the 
school  life  of  the  child  a  real  life.  Let  him  live  a  natural  life 
in  his  school  work.  Allow  him  to  do  things  that  will  make 
him  a  thinking  and  useful  citizen. 

At  this  stage  of  development,  the  child  is  not  capable  of 
forming  concise  and  exact  judgments;  therefore,  a  number 
of  exercises  have  been  arranged  for  the  teacher's  use.  These 
first  exercises  give  work  that  requires  what  we  may  term 
indefinite  or  loose  thinking.  As  the  teacher  proceeds  with 
the  exercises  the  child  is  led  to  see  equalities  and  hence  to 
think  and  to  reason  concisely  and  accurately.  Ruskin  says, 
"Finish  is  ruinous  because  it  sacrifices  better  things  than 
finish."  That  is,  the  process  of  learning  is  more  important 
than  the  finished  product;  logical  thinking  more  important 
than  the  facts  learned. 

The  Suggestive  Lessons  on  pages  xiii-xxii  are  symply  type 
lessons  to  be  varied  and  multiplied  at  the  discretion  of  the 
teacher.  A  great  variety  of  these  exercises  may  be  given  and 
a  great  deal  of  valuable  information  and  training  derived 
therefrom.  They  contain  the  three  great  mathematical  ideas, 
namely,  the  solid,  the  surface  and  the  line.  These  ideas  are 
taught  in  such  a  simple  way  that  the  child  grasps  them  and 
thus  lays  a  broad  foundation  for  his  higher  work.  They 
also  give  a  fine  opportunity  for  language  training  which  is 
so  necessary  for  logical  thinking.  For  instance,  in  measuring 
two  sticks  the  child  is  led  to  say,  ''This  stick  is  longer  than 
that  stick."  In  measuring  three  sticks  he  finds  one  to  be  the 
longest  and  another  to  be  the  shortest.  In  comparing  two 
oblongs— one  two  inches  long  and  the  other  four  inches  long— 
if  we  call  the  two-inch  oblong  one,  we  call  the  four-inch 
oblong  two.  If  we  call  the  four-inch  oblong  one,  we  call  the 
two-inch  oblong  one-half.    This  class  of  work  leads  the  child 


xii  Two  Years  Work  in  Numbers 

to  discover  finally  the  great  mathematical  principle  that  the 
value  of  a  number  depends  upon  the  unit  of  measure.  It  is 
suggested  that  much  attention  be  given  to  the  language  of 
mathematics  after  .the  child  has  been  in  school  a  sufficient 
time  to  feel  at  home  and  express  himself  freely.  Gentle  criti- 
cism is  always  the  best. 

Do  not  tell  the  child  to  memorize,  but  if  he  follows  the 
directions  given  in  the  exercises  he  Avill  learn  the  important 
facts  by  doing.  As  soon  as  the  child  is  capable,  allow  him  to 
copy  the  facts  to  be  learned ;  to  copy  a  fact  from  three  to  five 
times  before  copying  the  next  one.  There  is  a  strong  peda- 
gogical reason  for  this. 


SUGGESTIVE  LESSONS 


Note:  The  number  work  of  the  first  half  year  is  to  be 
presented  by  the  teacher,  the  book  not  being  placed  in  the 
hands  of  the  pupil  until  Part  One  is  reached,  which  will  be  at 
the  beginning  of  the  last  half  of  the  first  year.  The  work  to 
be  presented  by  the  teacher  during  the  first  half  of  the  year  is 
that  indicated  in  the  discussion  on  ''Sources  of  Material' * 
(pages  x-xii)  and  that  outlined  in  the  Suggestive  Lessons 
which  follow.  The  teacher,  of  course,  will  enlarge  upon  this 
material  as  she  may  deem  necessary. 

THINKING  EXERCISES 

The  material  below  forms  a  basis  for  several  lessons : 

Let  us  look  at  this  book.     (Holding  a  book  in  the  hand.) 
Name  things  in  the  school  room  that  are  larger  than  this 

book. 
Name  the  things  smaller  than  this  book. 
Name  some  things  in  your  home  that  are  smaller. 
Let  us  look  at  this  desk.     (Teacher's  desk.) 
Name  things  larger  that  you  saw  as  you  came  to  school. 
Name  things  at  home  larger  than  the  desk. 
Name  some  things  in  the  room  that  are  smaller  than  this 

chair. 
Count  the  windows  and  window  panes. 
Count  desks.    Count  books  on  the  teacher's  desk. 
Count  the  planks  in  the  floor. 
Let  us  see  how  far  each  one  can  count.   * 
Get  pages  of  children's  pictures  from  catalogues,  and  let  the 

pupils  count  the  objects  and,  for  seat- work,  allow  them 

to  color  some  of  the  pictures. 

xiii 


XIV 


Tivo  Years  Work  in  Numbers 


INDEFINITE  MEASUREMENTS 


Look  at  this  book.     (Pointing  to  the  one  in  the  hand.) 
Find  a  larger  one  in  the  picture. 
Find  one  a  little  smaller. 
Find  the  smallest  book. 
Find  the  largest  book. 
How  many  large  books  ? 
How  many  small  books  in  the  picture? 
Let  a  pupil  take  a  book  from  the  desk. 
Find  all  the  books  larger  than  this  one. 
Find  the  books  smaller  than  this  one. 
Count  the  larger  books. 
Count  the  smaller  books. 

Tell  a  nice  story  to  create  an  interest  in  books. 
Make  the  pictures  on  the  wall  the  basis  of  a  lesson  similar  to 
the  one  above. 


Let  each  child  bring  a  box  from  home. 
Place  the  boxes  on  the  table. 
Find  the  largest  box. 
Find  the  next  largest  box. 
Let  the  pupils  compare  these  boxes. 

(Watch  the  pupil's  language  and  try  to  have  it  improve  con- 
stantly, but  do  not  embarrass  him  in  doing  this.) 
Find  the  smallest  box. 
Let  a  pupil  compare  this  box  with  the  largest  box. 


Ejcplaiiatonj  cuid  Suggestive 


XV 


Let  pupils  compare  other  boxes. 

Think  of  things  at  home  smaller  than  the  largest  box. 

Count  the  large  boxes. 

Count  the  small  boxes. 

How  many  all  together  ? 

Take  four-inch  squares  and  make  boxes  for  seat  work   (see 

Exercise  9). 
Vary  this  work  for  several  lessons. 


The  material  that  follows  will  form  a  basis  for  a  number 
of  lessons: — 

Explain  edge  by  use  of  book. 

Find  edges  a  little  longer  than  this  edge  (pointing  to  the 
edge  of  the  book). 

Find  edges  much  longer  than  this  edge. 

Explain  horizontal  and  vertical  lines. 

Draw  a  book  and  show  that  edges  are  represented  by  lines. 

A  horizontal  line  is  a  'Mying-down"  line. 

A  vertical  line  is  a  *' straight  up-and-down"  line. 

Find  all  the  vertical  lines  in  the  school  room. 

Find  all  the  horizontal  lines  in  the  school  room. 

Count  ten  horizontal  lines. 

Count  10  vertical  lines. 

Count  horizontal  lines  in  the  windows. 

Count  the  vertical  lines  in  the  windows. 

Let  the  children  use  colored  sticks  to  make  figures  having  hori- 
zontal and  vertical  lines. 


Make  the  following  figures  on  the  board  and  have  the  pupils 
represent  them  with  colored  sticks  or  tooth-picks. 


e^ 


F 


Allow  children  to  do  original  work  in  laying  the  sticks. 
Never  lose  sight  of  the  artistic. 


XVI 


Two  Years  Work  in  Numbers 


The  following  lesson  is  suggestive  only  :— 

Take  a  square  of  paper. 

Hold  your  paper  up  in  front  of  you. 

How  large  a  square  have  you? 

How  many  corners  ?    What  kind  ? 

How  many  sides  has  your  paper? 

Point  to  the  upper  edge.    Lower  edge. 

Show  your  right  hand.     Left  hand. 

Point  to  the  right  edge  of  your  paper. 

Point  to  the  left  edge  of  your  paper. 

Point  to  the  upper  left  corner. 

Point  to  the  lower  left  corner. 

Hold  your  paper  by  the  right  edge ;  then  by  the  left  edge. 

Fold  these  edges  together.     Crease. 

What  is  the  shape  of  your  paper  ? 

AVe  may  call  it  a .    Keep  the  book  and  read  a  nice 

story  from  it. 
Have  the  children  think  of  the  story  for  the  next  day. 
The  following  day  make  some  pretty  drawings  in  the  book. 


Do  you  know  how  men  measure  these  edges? 

They  ur.e  a  foot  ruler  and  a  yard  measure. 

A  ruler  is  a  foot  long.     (Give  each  child  a  ruler.) 

It  takes  three  rulers  to  make  a  yard. 

Use  rulers  and  yard  stick  to  illustrate. 

Take  your  ruler  and  measure  this  edge  of  the  book. 

It  is  not  a  foot  long. 

We  must  learn  what  these  marks  mean  on  the  ruler. 

Count  1,  2,  3,  4,  5,  6,  7,  8,  9,  10,  11,  12. 


Explanatory  and  Suggestive  xvii 

Each  space  between  the  long  black  lines  is  inch.     How 

many  spaces  are  there? 
How  many  inches  on  a  ruler? 

inches  make  a  foot. 

Let  children  lay  their  inch  squares  by  the  ruler. 

Get  pages  from  catalogues  and  let  the   children  count  the 

pictures  of  men  and  women  and  then  color  them. 


LINEAR  MEASUREMENTS 


Find  the  longest  vertical,  or  up-and-down,  line. 
Find  the  next  longest ;  the  next  longest. 
Find  the  shortest  horizontal,  or  lying-down,  line. 
Find  the  next  shortest;  the  next,  etc. 
Find  the  longest  slanting  line. 
Find  the  next  longest;  the  next;  the  next. 
Count  the  vertical  lines. 
Count  the  horizontal  lines. 
Count  the  slanting  lines. 
Count  all  the  lines. 

Draw  similar  lines  on  the  board.     Give  the  children  much 
drill  in  judgment  forming  and  measuring. 


XVlll 


Two  Years  Work  in  Numh&rs 


LENGTHS 

Prepare  a  dozen  rough-cut  sticks. 
Find  the  longest  stick ;  the  shortest. 
Find  the  next  longest ;  next  shortest ;  etc. 
Find  two  sticks  of  the  same  length. 
Take  the  two  sticks  in  your  hands. 

This  stick  is than  this  one. 

IMeasure  the  longest  stick. 

It  is long. 

T^Ieasure  the  shortest  stick. 

It  is long. 

IMeasure  the  edges  of  teacher's  desk. 
Pleasure  the  edges  of  children's  desks. 
IMeasure  the  width    of  the  door. 

We  measure  things  with  the ruler  and  the 

measure. 

]\lake  the  following  with  colored  sticks  and  draw  with  crayons : 


The  exercise  that  follows  is  a  drill  in  getting  the  correct 
idea  of  length: — 

Hold  your  hands  1  foot  apart. 

Let  the  teacher  take  a  ruler  and  measure  the  space  between 

your  hands.     If  your  hands  just  touch  the  ends  of  the 

ruler  you  ''win  the  game." 
Hold  your  hands  2  feet  apart.     (Let  the  teacher  measure  by 

placing  2  rulers  together.) 


Explanatoi'}j  and  Siiyyestivc 


XIX 


Hold  your  hands  6  inches  apart.    IMeasure. 
Hold  your  hands  a  yard  apart.     Measure. 
Hold  your  hands  a  foot  and  a  half  apart.    Measure. 
Do  not  use  ruler  except  to  measure. 
Draw  on  the  board  a  line  2  feet  lon^:.    Measure. 
Draw  a  line  one  and  a  half  feet  long.    Measure. 
Draw  a  line  6  inches  long.     (Use  half  of  a  ruler.) 
Give  children  much  practice  in  drawing  the  horizontal,  ver- 
tical and  slanting  lines  on  the  board. 
With  your  sticks  at  your  desks,  make  the  following  figures : 


SURFACES 


Explain  surface  by  the  back  of  the  book. 

Find  smaller  surfaces  than  this  surface.     (Point  to  the  sur- 
face of  the  book.) 

Find  little  larger  surfaces  than  this  surface. 

Find  much  larger  surfaces  than  this  one. 

Find  surfaces  of  teacher's  desk.    Count  them. 

Count  surfaces  of  seats  in  the  room. 

Count    surfaces  of  desks,  chairs,  etc. 

Count  surfaces  of  windows. 

Think  of  surfaces  at  home,  larger  than  the  top  of  child's 
desk. 

Think  of  surfaces  at  home,  smaller  than  the  top  of  child's 
desk. 

Think  of  surfaces  you  saw  coming  to  school,  larger  than  the 
window ;  smaller  than  the  window. 
A  number  of  lessons  may  be  formed  from  these  suggestions. 

Allow  the  pupils  free  activity  in  moving  about. 


XX 


Tivo  Years  Work  in  Numbers 


Have  many  kinds  of  paper  surfaces  on  the  table. 


Find  the  largest  oblong 
or  rectangle. 

Find  another  like  it. 

Find  the  smallest  oblong. 

Find  another  like  it. 

Find  the  largest  triangle. 

Find  another  like  it. 

Find  the  smallest  circle. 

Find  another  like  it. 

Find  a  red  circle. 

Find  another  just  like  it. 

Find  a  green  square. 

Find  another  just  like  it. 

Find  a  red  triangle. 


Let  the  children  draw  the  oblongs  and  squares  and  color 
them.     Furnish  patterns. 

Draw  different  sized  oblongs  on  the  board  for  one  lesson. 
Give  another  lesson  on  triangles;  another  on  circles;  an- 
other on  squares. 

(A  box  of  colored  tablets  will  prove  useful  to  the  teacher.) 


Explanatory  and  Suggestive 


XXI 


INDEFINITE  MEASUREMENTS  OF  SURFACES 


D^O 


Find  real  surfaces  similar  to  these  figures. 
Find  the  largest  square  in  the  picture. 
Find  the  largest  rectangle. 
Find  the  next  largest  rectangle ;  the  next. 
Find  the  largest  triangle. 
Find  the  smallest  triangle. 
Let  the  pupils  compare  the  two. 
Find  the  largest  circle. 
Find  the  smallest  circle. 
Count  the  squares.     Count  the  circles. 
Count  the  triangles.    Count  all  the  figures. 
Draw  the  figures  and  color  them. 

Allow  the  children  to  use  patterns.     They  like  to  trace  de- 
signs and  to  color  them. 


Cut,  or  have  cut,  a  number  of  oblongs  one  inch  wide  and  two 
inches  long;  one  inch  wide  and  three  inches  long;  one  inch 
wide  and  four  inches  long;  one  inch  wide  and  six  inches  long; 


xxii  Two  Years  Work  in  Numbers 

one  inch  Avide  and  eight  inches  long;  one  inch  wide  and  nine 
inches  long. 

The  teacher  may  use  thes6  in  many  profitable  ways.  For 
instance,  take  the  two-inch  oblong  in  one  hand  and  the  four- 
inch  oblong  in  the  other  hand,  saying,  "If  I  call  this  one 
(holding  up  the  2-inch  oblong)  oyiCy  I'll  call  this  one  (hold- 
ing up  the  4-inch  oblong) .    Again:    If  I  call  this 

one  (holding  up  the  4-inch  oblong)  one,  I  shall  call  this  one 

(holding  up   the   2-inch  oblong)    .     A   great  variety  of 

comparison  work  may  be  done  with  these  simple  materials. 

Cut  or  have  cut  a  large  number  of  narrow  strips  to  use  iii 
the  development  of  the  beginning  number  work.  A  great 
deal  of  measuring  work  may  be  done  with  the  strips.  They 
may  be  broken  in  equal  parts  for  work  in  fractions.  They 
may  also  be  used  for  design  work. 

Materials  in  number  work  are  only  means  to  an  end.  Let 
them  be  simple  and  inexpensive. 

In  teaching  the   addition   facts,    use,   first,   the   following 
6 
form:      ^     Later  on  use  this  form:  6+2=8.     Have  many 

8 
sight  drills  on  the  addition  combinations,  using  the  first  form 
given  above.     Subtraction  facts  may  be  learned  by  the  same 
plan   (see  exercise  27). 


NOTES  ON  PART  ONE 


Note :  The  first  half  of  the  first  year  that  the  child  devotes 
to  the  study  of  mathematics  is  to  be  given  to  the  work  indi- 
cated in  the  discussion  on  ''Sources  of  Material"  (pages 
x-xii)  and  to  that  contained  in  the  "Suggestive  Lessons" 
(pages  xiii-xxii).  As  stated  before,  all  the  preceding  work  is 
to  be  presented  by  the  teacher.  The  formal  number  work  for 
the  child  begins  with  Part  One,  and  previous  to  this  time  the 
book  is  not  to  be  placed  in  his  hands. 


Notice  the  close  grouping  of  objects  in  Exercise  1.  Dis- 
tinguish the  idea  three  from  three  ones.  Let  the  teacher 
keep  the  twofold  idea  of  number  in  mind, — the  "how  much" 
and  the  "how  many;"  the  "content"  and  the  "ratio."  Also 
notice  that  the  exercises  on  each  new  number  use  ideas  that 
are  naturally  associated  with  that  number. 

It  is  presumed  that  the  child  knows  the  colors  and  their 
names.  The  teacher  will  kindly  assist  in  reading  the  lessons. 
This  will  not  detract  from,  but  add  to  the  interest  in  the 
number  discoveries. 

Observe  suggestions  for  seat  Avork  as  they  form  a  part  of 
the  plan  of  the  book. 

If  possible  use  objects  as  suggested.  You  will  discover 
that  the  inch  squares  have  been  used  more  frequently  than 
any  other  one  kind  of  objects.  Let  the  children  call  the  inch 
squares  many  different  things ;  as  cows,  horses,  chickens,  and 
fruits.  Use  the  inch  squares  to  show  all  the  "pairs"  of  each 
number  up  to  20.  Supplement  the  lessons  by  much  black- 
board work. 

Vary  the  work  as  suggested  in  Exercise  3.  Place  vertical, 
horizontal  and  slanting  lines  on  the  board.    Let  the  children 

xxiii 


xxiv  Two  Years  Work  in  Nimihers 

lay  sticks  to  represent  the  lines  on  the  board  and  then  have 
them  draw  these  lines  with  colored  crayons.  For  Exercise  8 
use  an  apple.  For  Exercise  7  use  a  yard  stick  and  a  foot  ruler. 
Let  children  make  large  boxes  for  use  in  taking  care  of  ob- 
jects for  their  number  work.  For  Exercise  11  use  the  meas- 
ures if  possible ;  if  not  possible,  use  drawings  on  the  board  to 
emphasize  the  drawings  in  the  book.  Also  use  drawings  to  aid 
the  pupils  in  computing  the  problems  which  use  the  units  of 
measure.  Let  the  child  do  much  comparison  work  as  sug- 
gested in  Exercise  12.  The  children  enjoy  the  building 
lessons  in  Exercise  13.  Make  baskets  any  size  you  wish,  as 
planned  in  Exercise  14.  Develop  the  signs  as  suggested  in 
Exercises  18,  24,  43. 

Let  the  childrn  draw  fruits  and  vegetables  on  heavy  paper. 
Color  the  drawings.  Cut  them  out  and  use  them  during  the 
winter  for  fruit  sales  as  suggested  in  Exercise  20.  Use  the 
buying  and  selling  game  frequently.  Often  have  tests y  revieivs 
and  drills.  Notice  how  the  multiplication  table  is  formed  in 
Exercise  25. 

Let  the  children  make  dominoes  as  suggested  in  Exercise 
29.  Use  these  dominoes  for  drill  work  in  addition  and  sub- 
traction. They  may  be  used  as  checks  with  which  to  draw 
the  toy  money  from  the  bank.  Let  the  small  children  buy 
and  sell,  paying  one  cent  for  their  objects.  This  gives  much 
practice  in  counting  by  ones.  Then  they  will  learn  to  count 
by  twos,  threes  and  fours  as  the  work  advances. 

If  the  little  children  cannot  make  the  strips  as  suggested 
in  Exercise  30,  allow  the  older  children  to  make  them  for  the 
little  ones.  The  great  spirit  of  modern  education  is  con- 
tained in  the  expression,  ' '  Help  ye  one  another. ' ' 

Notice  how  the  multiplication  table  begins  in  Exercise  43 
and  that  the  same  plan  is  carried  through  the  book. 

After  the  child  has  mastered  the  multiplication  table  in 
this  form,  allow  him  to  make  the  tables  of  2's,  3's  and  4's  as 
the  work  advances. 


NOTES  ON  PART  TWO 


Kindly  study  carefully  the  Preface,  Explanatory  and 
Suggestive,'  and  Part  One  before  beginning  work  on  Part 
Two.  You  will  find  that  such  study  is  a  direct  and  necessary 
preparation  for  the  successful  teaching  of  Part  Two. 

Use  carefully  the  device  in  the  first  exercise  of  Part 
Two.  Use  all  the  ideas  given  in  this  exercise  to  impress  the 
child  that  eleven  is  one  te)i  and  one  luiit.  Also  lead  him  to 
see  that  it  requires  two  or  more  places  to  write  the  numbers 
above  9. 

Let  the  children  use  the  "buying  and  selling"  game  of- 
ten. Do  not  forget  to  review  and  drill.  Give  a  number  of  les- 
sons using  toy  money.  Use  Avork  in  Exercise  13  often, — until 
the  forty-five  addition  facts  are  mastered.  Give  much  work  as 
suggested  in  Exercise  80.  This  work  will  prepare  the  child  for 
short  division.  It  is  as  necessary  for  the  child  to  recognize 
22  as  the  multiple  of  the  two  factors  11  and  2  as  it  is  for 
him  to  knoAV  that  2  times  11  are  22.  For  instance,  if  he  is 
dividing  24  by  11  he  must  see  the  multiple  22  before  he  can 
get  the  answer  2.  In  teaching  the  multiplication  facts 
8X3=24  and  9X4=36,  give  the  following  forms:  8X3=?; 
9x4=?;  8X?=24;  9X?=36;   ?x?=24;   ?X?=36/ 

Drill  on  multiplication  and  division  at  the  same  time,  just 
as  you  teach  subtraction  by  addition.  If  the  child  knows  the 
two  component  parts  of  a  number  he  can  subtract  or  divide 
as  readily  as  he  can  add  or  multiply.  Kindly  use  the  plan  of 
the  book  to  teach  the  multiplication  table. 

If  the  child  cannot  make  the  concrete  problems  asked  for 
in  exercise  89,  give  more  work  on  the  preceding  exercises. 

Part  Two  of  the  book  may  be  continued  in  the  Third  Grade 
if  so  desired.  Follow  the  same  plan,  using  a  variety  of  ma- 
terial to  teach  these  fundamental  facts  and  processes.     Have 

XXV 


xxvi  Two  Years  Work  in  Numbers 

the  pupils  write  the  figures,  words  and  Roman  numerals  as 
you  take  up  the  new  numbers.  Use  the  form  in  Exercise  97. 
Insist  upon  the  moving  of  the  inch  squares  just  as  you  direct. 
Show  the  difference  between  a  row  and  a  column.  The  inch 
squares  may  be  cut  at  any  printing  office. 


PART  ONE 


MINUTES 

"We  are  but  minutes,  little  things, 
Each  one  furnished  with  sixty  wings, 
With  which  we  fly  on  our  unseen  tracks 
And  not  a  minute  ever  comes  back. 

We  are  but  minutes,  use  us  well. 
For  how  we  are  used  you  must  one  day  tell ; 
Who  uses  minutes  has  hours  to  use, 
Who  loses  minutes  whole  years  must  lose. 


Two  Years  Work  in  Numhers  3 

Exercise  1 


/ 


(7?W 


2 


ytwV 


3 


4 


S 


Two  Years  Wvrk  in  Numbers 
Exercise  2 


w 


Count  to  10.         Count  to  20. 

How  long  is  line  A? 

How  long  is  line  B  ? 

How  long  is  line  C  ? 

How  long  is  line  D  ? 

How  long  is  line  E  ? 
How  much  longer  is  line  B  than  line  A? 
Plow  much  longer  is  line  D  than  line  B  ? 
How  much  shorter  is  line  A  than  line  C  ? 

Use  ruler  and  colored  sticks  to  measure 
these  lines.  Place  colored  sticks  in  same 
order  as  lines  above  and  draw  with 
crayons. 


Tivo  Years  Worlc  in  Numhcrs  5 


Exercise  3 

Have  colored  sticks  on  the  table. 

Teacher  takes  a  5-inch  stick. 

Find  a  stick  as  long  as  this  one. 

Measure  sticks  each  time  after  choosing.  Use  ruler 
if  you  wish. 

Take  a  2-inch  stick.    Find  one  just  like  this. 

Take  a  3-inch  stick.    Find  one  just  like  this. 

How  long  is  each  stick?     How  many  sticks  have 
you  now  ? 

Count  all  the  sticks  the  children  have. 

(When  the  child  gets  the  correct  stick  he  wins  the 
game.) 

(When  he  does  not,  the  teacher  wins  the  game.) 

Count  to  50  and  backwards. 

Note  : — V  arv  this  work  in  a  number  of  wavs. 


Two  Years  Work  in  Numhera 
Exercise  4 


^-|  xi/ncL  I— I  MyL£^    I— I      1—1 


M/nd(m)  mAjZ' 


y%xinixi(^ni%>o!Mj2^0f^ 


We  have  head. 

We  have  nose.  We  have  month. 

We  have  eyes.  We  have  hands. 

We  have  arms.  We  have  feet. 

gloves  make  a  pair.    shoes  make  a  pair. 

Copy  the  drawings  in  this  exercise. 


Two  Years  Work  in  Numbers  7 

Exercise  5- 
Copy  the  following  number  facts : 

1  2  3  2  3  4 

j_     j^     j_     _2     ^      i 

2  3  4  4  5  5 
Write: 

1  inch  and  1  inch  are inches. 

2  inches  and  1  inch  are inches. 

2  inches  and  2  inches  are inches. 

3  inches  and  1  inch  are inches. 

3  inches  and  2  inches  are inches. 

4  inches  and  1  inch  are inches. 

3  fans  and  2  fans  are fans. 

4  chairs  and  1  chair  are chairs. 

aynd%m%  a/i3 
ma/nd%%m  ayiJ2y 


8                Two  Years  Work  in  Numbers 
^    Exercise  6 
^         X  X        has  sides. 

lias  little  leaves. 


lias  — —  sides. 


has 


panes. 


An 


has  sides. 


has  — —  sides. 


has 


corners. 


has  points. 


has  fingers. 


Tivo  Years  Work  in  Numbers  9 

Name  4  kinds  of  leaves.    Bring  other  leaves  and 

count  their  points. 
Of  what  does  a  triangle  remind  you?     Of  what 

does  the  square  remind  you  ? 
Find  similar  surfaces  in  the  room. 


Exercise  7 


1 1 1 1 1 1 1 1 1 1 1 1 1     orw 


on£. 


The  long  stick  is  a  yard  stick.    It  is  a  yard  long. 

A  yard  is feet  long. 

One-third  of  a  yard  is foot. 

One-half  of  a  yard  is foot  and . 

One  foot  is of  a  yard. 

Two  feet  are of  a  yard. 

Three  feet  are of  a  yard. 

We  measure  feet  with  a  ruler. 

A  ruler  is  a  foot  long. 

rulers  laid  end  to  end  make yard. 


A  yard  is long. 

Name  five  things  we  measure  by  the  yard. 
Name  five  things  we  measure  by  the  foot. 


10 


Two  Years  Work  in  Numbers 


Exercise  8 


We  have  an  apple  in  the  picture. 

If  we  cut  our  apple  into  two  equal  parts  we  call 
each  part  one-half. 

One-half  of  an  apple  and  one-half  of  an  apple  make 
one  whole  apple. 

If  we  cut  our  apple  into  three  equal  parts  we  call 
each  part  one-third. 

One-third  and  one-third  make  two-thirds. 

One-third  and  one-third  and  one-third    make    the 
whole  apple. 

How  many  thirds  make  a  whole  apple  ? 

Note  : — Let  the  children  cut  other  whole  things 
into  halves  and  thirds. 


Two  Years  Work  in  Numbers 


11 


Exercise  9 


PATTERN  FOR  A  BOX 

Take  a  4-iiich  square.  Lay  this 
square  even  with  the  edge  of  your 
desk.  Fold  lower  edge  to  the  upper 
edge.  Crease  and  unfold.  Fold 
right  edge  to  left  edge.  Crease  and 
unfold. 


-r \ 

Box 


How  many  squares  have  you  now?  What  part 
of  the  large  square  is  the  small  square? 

Crease  and  unfold  after  each  folding. 

Fold  the  lower  edge  to  the  middle ;  upper  edge  to 
the  middle ;  left  edge  to  the  middle ;  right  edge  to 
the  middle. 

How  many  squares  have  you  now  ? 

Cut  the  paper  where  the  heavy  marks  are  in  the 
picture.  Fold  the  corner  squares  inside  and  paste 
them. 

How  many  corners  has  your  box?  How  many 
edges  ?  How  many  faces  ?  Which  is  the  largest 
face?  How  much  larger?  Point  to  the  longer 
edges?    How  much  longer  are  they?     - 


12 


Two  Years  Work  in  Num'bers 


Exercise  10 


I  have  four  one-inch  squares  in  a  row. 

My  row  is inches  long  and inch  wide. 

2  square  inches  and 

square  inches  are 

square  inches. 

I  of  4  square  inches  is 
— -  square  inches. 

Move  one  inch  square 
below. 

3  square  inches  and 

square  inch  are  

square  inches. 


We  have 


seasons.    Name  them. 


Name  4  things  used  on  the  farm.    Name  4  things 

we  get  from  the  farm  to  eat. 
Arrange    colored   squares    in    designs,    trace    the 

squares  and  color  them. 


Two  Years  Work  in  Numbers 


13 


Exercise  11 


C  5?  O'  QP 


/?na^        /  ^^7y{/7at' 


2,  y/u/Tn^ 


/ 


^ 


/TtuzAji^ 


/ 


14 


Tivo  Years  Work  in  Ntimhers 


Exercise  12 


B 


The  square  A  is  an square. 

The  square  B  is  a square. 

Each  side  of  square  A  is  inch. 

Each  side  of  square  B  is  inches. 

The  squere  A  has  corners. 

The  square  B  has  corners. 

The  square  A  is  square  inch. 

The  square  B  is  square  inches. 

How  much  larger  is  square  B  than  square  A 
Draw  the  squares  and  color  them. 


Two  Years  Work  in  Numbers  15 

Exercise  13 

Use  small  objects  for  pigs  and  chickens. 

Build  a  pen  with  four  sides,  four  sticks  high. 

Put  four  pigs  in  the  pen. 

Feed  each  pig  four  grains  of  corn. 

Let  the  pen  down  at  one  corner. 

Drive  one  pig  out. 

How  many  pigs  in  the  pen  ? 

Drive  2  pigs  out  of  the  pen. 

How  man}^  pigs  in  the  pen  ? 

Build  another  pen  with  five  rails. 

Put  five  chickens  in  the  pen. 

Feed  each  chicken  five  grains  of  corn. 

Let  the  pen  down  at  the  corner. 

Drive  three  chickens  out  of  the  pen. 

How  many  chickens  in  the  pen  ? 

Drive  out  two  chickens. 

How  many  chickens  now  ? 


16  Two  Years  Work  in  Nitmhers 


Exercise  14 


Would  you  like  to  make  a  basket? 
Fold  your  square  just  as  you  did 
for  your  box. 

Cut  one  row  of  squares  off.     How  many  squares 
have  you  cut  off  ? 

How  many  squares  have  you  now? 

How  many  corners  ?    How  many  edges  ? 

Now  cut  your  oblong  as  you  did  for  the  box. 

Fold  corners  inside  and  paste. 

Cut  a  narrow  handle  and  paste  on  the  inside. 

Name  4  things  that  baskets  are  made  of. 

Name  5  things  that  we  carry  in  baskets. 

In  what  kind  of  business  do  men  use  baskets  ? 

What  would  you  like  to  put  in  your  basket  ? 


Write  the  following 

AoaoM 


Two  Years  Work  in  Numbers 


17 


Exercise  15 


A  Bushel 

4  pecks  make  1  bushel. 

2  pecks  make  one-half  bushel. 

2  pecks  and  2  pecks  make bushel. 

3  pecks  and  1  peck  make bushel. 

Name  things  we  measure  by  the  peck  and  bushel. 
Count  to  50. 

Write: 


18  Two  Years  Work  in  Numbers 

Exercise  16 

1  2  2  3  2  4 

i_  J_  A  i_  A  i. 

2  3  4  4  5  5' 

We  call  these  the  ^^ pairs"  of  2,  3,  4  and  5.  . 

Count  to  100. 

Go  to  the  board  and  show  the  pairs  of  4  with  dots. 

Make  short  vertical  lines  to  show  the  pairs  of  five. 

Make  circles  to  show  the  pairs  of  4. 

Two  pairs  of  shoes  are shoes.    Two  pairs  of 

gloves  are gloves. 

Two  pairs  of  eyes  are  eyes,     Two  pairs  of 

hands  are hands. 

John  had  4  shoes  and  gave  one  pair  to  a  poor  boy. 
He  then  had shoes. 

Paul  had  5  pencils  and  lost  2  of  them.    He  now  has 


AVrite  these  numbers : 

1,  2,  3,  4,  5,  6, 7,  8,  9, 10,  11, 12, 13, 14, 15, 16, 17, 
18,  19,  20. 


Two  Years  Work  in  Numhers  19 

Exercise  17 

ONE  Y  ONE VoNeV  one  Y  ONE 

centAcentA  cent  a  cent  a  cent 

V 

CENTS 

Five  pennies  make  one  nickel. 

Count  by  5  's  to  50. 

one-cent  pieces  make  a  nickel. 

3  cents  and  2  cents  are  cents. 

4  cents  and  1  cent  are  cents. 

5  cents  less.  2  cents  are  cents. 

5  cents  less  4  cents  is  cent. 

2  nickels  are  one  dime. 

5  dimes  less  2  dimes  are  dimes. 

5  dimes  less  3  dimes  are  dimes. 

A  nickel  is cents.    A  dime  is nickels. 

Make  one-cent  pieces  and  five-cent  pieces  for  future 
use  in  buying  and  selling. 


20 


Tivo  Years  Work  in  Numbers 


Write : 


Exercise  18 

We  have  five  inch  squares  in  a  row. 
Move  one  inch  square  below. 

4  inch  squares  and  inch 

square  are inch  squares. 

Move  two  inch  squares  below.     3 

inch    squares    and    incli 

squares  are inch  squares. 

3  and  2  are  . 

3    +    2  are  . 

3    +    2    =    . 

5  less  3  are . 

5-3  are . 


5    -    3  =  . 

+    means  and,    -  means  less, 
=  means  are  and  sometimes  is, 


3  2 
1          _2 

4  4 


3  4 

5  5 


Two  Years  Work  in  Numbers  21 

Exercise  19 

(1)  We  can  buy two-cent  stamps  for  four 

cents. 

(2)  We  can  buy  penny  pencils  for  four 

cents. 

(3)  Mary  had  5  nickels  and  lost  two  of  them. 
She  now  has nickels.  She  can  buy pen- 
cils at  5  cents  apiece. 

(4)  For  one  nickel  we  can  buy  a  tablet.  Two  tab- 
lets cost dime  or . 

(5)  James  has  2  pets  in  one  room  and  3  in  an- 
other room.    In  both  rooms  he  has pets. 

(6)  The  mother  hen  had  5  little  chicks.  4  of 
them  died.     She  now  has chick. 

Write  pairs  of  the  numbers  2,  3,  4  and  5. 

Exercise  20 

A  FRUIT   SALE 

Let  each  child  bring  fruit  for  the  sale. 

Use  pennies  made  by  the  children. 

What  are  the  prices  of  bananas  and  grapes  ? 

'^I  want  a  banana.     I  shall  pay cents." 

^  ^  I  '11  buy  a  bunch  of  grapes.    I  '11  pay cents. ' ' 

' '  I  want  a  pear.    I  shall  pay cents. ' ' 

' '  I  wish  an  apple.    I  shall  pay cents. ' ' 


99 


Tivo  Years  Work  in  Numbers 


' '  I  wish  two  oranges.    I  shall  pay cents. ' ' 

' '  I  want  2  lemons.    I  shall  pay cents. ' ' 

' '  I  want  2  peaches.    I  shall  pay cents. ' ' 

' '  I  wish  3  plums.    I  ^hall  pay cents. ' ' 

^^I  want  2  bananas.    I  shall  pay cents." 

^^I  want  2  bmiches  of  grapes.     I  shall  pay  

cents. 

^  ^  I  want  3  apples.    I  shall  pay cents. ' ' 

Now,  children,  you  may  make  paper  fruit  to  look  as 
much  like  the  real  fruit  as  you  can,  and  use  it 
for  fruit  sales  during  the  winter. 

Exercise  21 


A  cube  has  — 

Each  face  has 

face  has  — 


faces. 

—  corners. 


Each 


angles. 


Count  the  corners  on  the  cube. 
Count  the  edges  on  the  cube. 
We  have  6  one-inch  cubes  in  a  row. 
Our  row  is inches  long  and  — 


wide  and 


high. 


Two  Years  Worh  in  Numbers 


23 


We  can  see faces,    llow  many  faces  of  cubes 

are  not  seen  ? 
When  we  take  away  four  cubes,  Ave  have cubes 

left. 
We  again  place  them  in  two  equal  roAvs. 

One-half  of  six  cubes  is cubes. 

One-third  of  six  cubes  is cubes. 

Two-thirds  of  six  cubes  are cubes. 

Let  the  children  make  cubes  of  paper.    Use  pattern 

in  Exercise  22. 


n^ 

I 

Exercise  22 


Fi^m 


7 ' 

} « 


Take  a  four-inch  square.  Fold  it  the  same  as  for 
the  box. 

Cut  off  one  row  of  squares.  Cut  paper  where  heavy 
lines  show  in  figure  II. 

Fold  squares  in  shape  of  a  cube,  and  paste  the  sides 
together. 

A  neater  and  more  artistic  plan  is  shown  in  figure 
III.  If  you  use  stiff  paper,  use  this  plan.  Cut 
as  figure  III  shows,  and  paste  flaps  in. 


24  Two  Years  Work  in  Numbers 


Exercise  23 

We  have inch  squares  in  a  row. 

Move  two  inch  squares  below. 

4  inch  squares  and inch  squares 

are inch  squares. 

Move  one  inch  square  above. 

1  inch  square  and inch  squares 

are inch  squares. 

Move  two  inch  squares  below\ 

3  inch  squares  and inch  squares 

are inch  squares. 

There  are threes  in  6. 

There  are  twos  in  6. 

J  of  6  is  3.  f  of  6  are  6. 

J  of  6  is  2.  f  of  6  are  4. 

5  3  4 

1  A  A 

6  6  ~6 

Copy  each  addition  fact  five  times. 


Two  Years  Work  in  Numbers 


25 


Exercise  24 
Copy  each  of  the  following  problems  three  times : 
123234453 

¥¥4455666 

Use  a  dozen  objects  and  a  foot  rule. 

6  is dozen. 

6  inches  is of  a  foot. 

6  months  is of  a  year. 

There  are  — —  working  days  in  a  week. 

2  times  3  are  6. 


3  are  6. 
3  =  6. 

1  =  ? 
1  =  ? 
1  =   ? 


3  times  2  are  6. 

3      X 

2  are  6. 

3       X 

2  —  6. 

2       X 

2  —   ? 

2       X 

1  —   ? 

3       X 

1  —  ? 

+   means  times  or  muUipUed  by, 
=  means  are  or  sometimes  is. 
Count  by  fives  to  100. 
Count  by  tens  to  100. 

(1)  Clyde  has  6  apples.    He  gives  each  friend  2 
apples  till  all  are  gone.    He  has friends. 

(2)  Charles  gathered  4  quarts  of  cherries.  Mary 
gathered  2  quarts.    They  both  gathered quarts. 

(3)  Thomas  bought  6  tablets  and  sold  5  of  them. 
He  now  has tablet.- 


26  Two  Years  Work  in  Niimhers 


Exercise  25 

table  three 

times : 

1 

One 

I 

2 

Two 

II 

3 

Three 

III 

4 

Four 

IV 

5 

Five 

V 

6 

Six 

VI 

1x1  =  1. 

2x1  =  2. 
3x1  =  3. 
4x1  =  4. 
2x2  =  4. 
5x1  =  5. 
2x3  =  6. 
6x1  =  6.        Count  by  2 's  to  6.  Count  by  3 's  to  6. 

2  cents  and  3  cents  are cents. 

4  apples  and  2  apples  are apples. 

3  dimes  and  3  dimes  are dimes. 

5  oranges  and  1  orange  are oranges. 

(1)  If  two  boys  divide  6  apples  equally,  each 
boy  will  take apples. 

(2)  One-half  of  6  apples  is apples. 

(3)  One-third  of  6  apples  is apples. 

(4)  Two-thirds  of  6  apples  are apples. 

(5)  Delmar  can  buy  3  two-cent  stamps  for 

cents. 

(6)  If  one  post  card  costs  3  cents,  what  will  2 
post  cards  cost  ? 

(7)  One-half  of  a  foot  is inches.  One-quar- 
ter of  a  foot  is inches. 

(8)  3  boys  were  drawing  on  the  blackboard,  and 
3  were  working  problems.  How  many  boys  were  at 
work? 


Two  Years  V>^ork  in  Numbers 
ABC 


27 


Exercise  26 

How   large    is    the 
square  ? 

How  long  is  the  ob- 
long marked  B  ? 

How  long  is  the  ob- 
long marked  C  ? 

The  long  oblong  is 

times  as  long 

as  the   short  ob- 
long. 

The  oblong  marked  B as 

long  as  the  oblong  marked  C. 

3  square  inches  are of  six 

square  inches. 

1  square  inch  is of  three 

square  inches. 

How  many  square  inches  can  you 
make  out  of  the  short  oblong? 

How  many  out  of  the  long  one  ? 


28  Two  Years  Work  in  Numbers 

Exercise  27 

TEST 

2  +  3=?  4-2=?  1  2 
4  +  1  =  ?  2  +  2  =  ?  1  2 
6-4=?  3-3=? 

3  +  3=?  5-1=? 
6-3=?  4  +  3=?  1         2 

4  +  2=  ?  6-2=  ? 
3x2=?  4x1=? 
2x2=  ?  3x1=  ? 
5x1=?  1x5=?  1        2 


1        2 

1        2 
1        2 


1  2 

1  2 

1  2 

1  2 


Change  addition  facts  to  two  subtraction  facts,  as 
shown  below. 


2 

4 

4 

2 

5 

5 

+2 

-2 

-2 

+3 

-2 

--3 

4 

6 

6 

3 

4 

4 

+2 

-4 

-2 

+1 

-3 

-1 

5 

6 

6 

4 

5 

5 

+1 

-5 

-1 

+1 

-4 

-1 

2 

3 

3 

3 

6 

6 

+1 

-2 

-1 

+3 

-3 

-3 

Tivo  Years  Work  ui  Niimhers 


29 


Exercise  28 


JFigT 

F{^IE 

I              1              1 
1              1              1 

1 ,             •              1 1 

i  1                 •                 'i  1 

•  I                 '                 '  * 
-;* i |"J 

I  «              '              '  !. 

I '              '               '  1 
I  (              '                , 

:i J J. 

--" 

• 

1            1            1 
1            '            ' 

J ! L 

Box 


Lid 


Take  a  six-inch  square  of  thick  paper. 

Lay  the  square  even  with  your  desk. 

Fold  the  lower  edge  to  the  upper  edge  and  press  the 

fold.     Unfold. 
Fold  the  right  edge  to  the  left  edge.    Crease  and 

unfold. 
Fold  the  lower  edge  to  the  middle  and  crease.  Fold 

the  upper  edge  to  the  middle  and  crease.    Un- 
fold. 
Fold  the  right  edge  to  the  middle  and  crease.  Fold 

the  left  edge  to  the  middle  and  crease.  Unfold. 
For  the  box,  cut  the  dark  lines  as  shown  in  figure  I. 

Fold  and  paste. 
For  the  lid  do  not  make  the  last  folds  quite  to  the 

middle. 
Cut  the  heavy  lines  as  shown  in  figure  II.    Fold 

and  paste. 


30 


Two  Years  Work  in  Numbers 


Exercise  29 


• • 

•        •    • 


Make  three  dominoes  of  each  kind. 


Write 


C£/nXd 


AA/z    Ajyi^e/n 


There  are 
There  is  — 


There  are 
There  are 

2 

7 


—  days  in  a  week. 

four  in  7  and over. 

—  twos  in  7  and over. 

—  threes  in  7  and over. 


7 

-5 

2 


7  7 

-2        -1 

5  6 


Write  pairs  of  2,  3,  4,  5  and  6. 

Count  by  tens,  beginning  with  1,  2,  3,  4,  and  5. 


Tivo  Years  Work  in  Niinihers  31 

Exercise  30 

Cut  7  strips  7  inches  long  and  1  inch  wide. 

One  strip  contains square  inches. 

3  strips  and  4  strips  are strips. 

2  strips  and  5  strips  are strips. 

6  strips  and  1  strip  are strips. 

Take  a  strip  and  fold  it  end  to  end.    Cut  it  in  two 
pieces. 

One-half  of  7  inches  is inches. 

Take  another  strip  and  see  how  many  two-inch 

strips  you  can  make.    What  have  you  left  ? 
Take  another  strip  and  see  how  many  three-inch 

strips  you  can  make.    What  have  you  left  ? 

Copy  the  following  five  times : 


3 

5 

6 

7 

7 

7 

7 

4 

2 

1 

-4 

-5 

-6 

-3 

7 

7 

7 

3 

2 

1 

4 

7 

7 

6 

6 

6 

6 

5 

-2 

-1 

-6 

-1 

-4 

-3 

-2 

5 

6 

0 

5 

2 

3 

3 

Write  these  words : 


32  Two  Years  Work  in  Numbers 

Exercise  31 

Use  ruler  to  measure  after  drawing. 

Draw  a  line  seven  inches  long. 

Draw  a  line  one-half  of  7  inches.    How  long  is  it  ? 

Draw  a  line  a  foot  long.    What  is  one-half  of  this 
line? 

How  many  inches  in  a  foot  ? 

How  much  longer  is  your  7-inch  line  than  your  6- 
inch  line  ? 

3  rulers  laid  end  to  end  make  a . 


Draw  a  3-foot  line.    Give  this  line  another  name. 

What  do  we  measure  by  the  yard  ? 

What  do  we  measure  by  the  foot  ?     - 

Write  numbers  from  1  to  50. 

Write  numbers  from  2  to  50  by  twos. 

3  inches  and inches  are  7  inches. 

5  inches  and inches  are  7  inches. 

6  inches  and inch      are  7  inches. 

4  inches  and inches  are  6  inches. 

2  inches  and inches  are  5  inches. 


T'wo  Years  Worl:  in  Xumhers  33 

Exercise  32 


^ 


Prism 

A  prism  has ends  and sides.    The  ends 

are . 

If  we  put  our  prism  in  the  sunlight,  we  see  the  col- 
ors of  the  rainbow. 
The  prism  shows  7  colors. 
The  7  colors  are  violet,  indigo,  blue,  green,  yellow 

orange  and  red. 
I  have  seen colors  on 

plants. 
I  have  seen colors  on 

birds. 
I  have   seen  colored 

dresses. 
I  have   seen  colored 

houses. 

Exercise  33 

(1)  7  bovs  were  playing  hide  and  seek.  3  boys 
were  found.    How  many  were  not  found  ? 

(2)  5  girls  were  playing  with  dolls.  Each  girl 
had  one  doll.  Jennie  came  and  brought  2  more 
dolls.    How  many  dolls  have  they  now? 

Count  by  tens,  beginning  mth  seven. 

(3)  Mary  has  7  yards  of  lawn  for  2  doll  dresses. 
Each  dress  will  require yards. 


34  Two  Years  Work  in  Numbers 

(4)  7  birds  were  on  the  fence.    2  birds  flew  away. 
How  many  are  on  the  fence  ? 

(5)  7  girls  belonged  in  the  reading  class.    1  girl 
was  absent.    How  many  girls  were  present  ? 

(6)  A  boy  had  7  marbles  in  his  pocket  but 
lost  6.    How  many  had  he  left  ? 

Copy  each  pair  of  numbers  that  make  7,  five 
times. 

Exercise  34 

(1)  In  a  week  James  spends  5  days  in  school  and 
days  at  home.     Name  the  days  he  spends  at 


school.    Name  the  days  he  spends  at  home. 

(2)  If  John  had  5  arrows  and  made  2  more,  he 
would  then  have arrows. 

(3)  Ruth  had  7  apples  and  gave  1  apple  to  each 
of  3  boys.    She  then  had applet. 

(4)  Helen  drew  7  pictures  and  lost  4  of  them. 
She  had pictures  left. 

Count  by  tens  to  103,  beginning  with  3. 
Copy  the  following : 

3  5  6  3  4  4  2 

_4        _2        J.        _3        ^        _1        _2 

7  7  7  6  6  5  4 


The  first  day  of  the  week  is . 

The  seventh  day  of  the  week  is . 

Name  the  days  of  the  week.    Name  7  games. 


Tivo  Years  Work  in  Numbers 


35 


Exercise  35 


This  oblong  is  inches  wide  and 

long. 


inches 


The  two  ends  are 
inches. 


inches.    The  two  sides  are 


If  we  move  our  pencil  around  this  oblong  it  will 
travel inches. 

4  square  inches  and  4  square  inches  are square 

inches. 

One-half  of  8  square  inches  is square  inches. 

One-fourth  of  8  square  inches  is square  inches. 

Write: 


36  Two  Years  Work  in  Numbers 


Exercise  36 


You  have  made  circles  with  patterns. 

We  can  make  circles  of  any  size  we  wish  with  a 
circle-maker.    I  shall  tell  you  how. 

Cut  a  strip  of  thin  pasteboard  6J  inches  long  and 
one-half  inch  wide.  Measure  the  inches  and  half 
inches.    Mark  the  inches  by  lines  across  the  strip. 

Mark  the  half  inches  by  lines  half  across  the 
strip.  Punch  a  hole  in  each  line  in  the  center  of  the 
strip. 

Place  a  pin  in  one  hole,  sticking  it  through  your 
paper.  Place  your  pencil  point  in  another  hole, 
the  distance  away  from  the  pin  being  half  the  size 
of  the  circle  you  wish  to  make.  Whirl  your  circle- 
maker,  and  you  will  have  a  perfect  circle. 


Two  Years  Worlx  in  N umbers  37 

Exercise  37 

Cut  an  oblong  8  inches  long  and  4  inches  wide. 

Lay  it  even  with  the  edge  of  the  desk. 

Fold  the  lower  edge  to  the  upper  edge. 

How  wide  is  your  oblong  ? 

Open  and  fold  right  edge  to  left  edge. 

How  many  oblongs  ? 

Open  and  fold  right  edge  to  the  middle. 

Fold  left  edge  to  the  middle. 

How  many  squares  have  you  now "? 

Draw  a  circle  in  each  square. 

How  many  circles  have  you  ? 

How  wide  is  your  circle  ? 

8  circles  less  4  circles  are circles. 

8  circles  less  3  circles  are circles. 

8  circles  less  6  circles  are circles. 

8  circles  less  7  circles  is circle. 

8  circles  less  5  circles  are circles. 

Count  bv4's  to  100. 


38 


Two  Years  ]]^ork  in  Numbers 


Exercise  38 


Make  3  of  each  domino. 
2  pints  make  1  quart. 
4  quarts  are  — —  pints. 
4  gills  make  one  pint. 

2  pints  are gills. 

8  gills  are pints. 

8  pints  are quarts. 

4  pints  and  4  pints  are 

5  pints  and  3  pints  are 
2  gills  and  6  gills  are  - 


4  +  4 

5  +  3 

2  +  6 

1  +  7 

3  +  4 

4  +  2 

5  +  2  = 


=  ? 
=  ? 
=  ? 
=  ? 


quarts, 
pints. 


—  pints. 

1  quart  and  7  quarts  are  quarts. 

2  pints  and  6  pints  are  quarts. 


Two  Years  Work  in  Numbers 


39 


Exercise  39 


a/t^^ 


oAjt' 


a/te^ 


a/t£^ 


6  +  2 
5  +  2 

4  +  2 


8  less  2  are 

8  less  4  are 

8  less  5  are 

8  less  1  are 

There  are  - 
There  are  - 
There  are  - 


7  +  1  = . 

5  +  3  = . 

4  +  4  = . 

8  less  6  are 
8  less  4  are 
8  less  3  are 
8  less  7  is  - 


twos  in  8. 
fours  in  8. 
threes  in  8  and 


over. 


5  sticks  and  2  sticks  are 
4  sticks  and  4  sticks  are 


sticks, 
sticks. 


40  Two  Years  Work  in  Numbers 

Exercise  40 


We  have  cut  an  8-inch  square. 

We  have  cut  an  8-inch  circle  from  the  square. 

We  may  call  the  circle  a  pie. 

We  cut  the  pie  into  two  equal  parts. 

One  part  is  called . 

We  now  cut  the  pie  into  four  equal  parts. 

We  call  each  part  a  quarter  or . 

Now  let  us  cut  one  pie  into  eight  equal  jmrts. 

Each  part  is  called  one . 

If  we  take  away  4  parts  we  have parts  left. 

Place  the  parts  together  again. 

If  we  take  away  8  parts  we  have parts  left. 


Tivo  Years  Work  in  Niimhers 


41 


Exercise  41 


T\        r 


A  Peck 


A  Peck 


8  quarts  make  a  peck. 

4  quarts  make peck. 

1  peck  makes quarts. 

One-half  peck  makes quarts. 

6  quarts  and  2  quarts  are quarts  or 

3  quarts  and  5  quarts  are quarts  or 

4  quarts  and  4  quarts  are peck. 


7  quarts  and  1  quart  are 
One-fourth  of  a  peck  is  - 


-  quarts 
quarts. 


pecks  make  a  bushel. 

8  pecks  make bushels. 

2x4  pecks  make  bushels. 

5  +  3  pecks  make bushels. 


peck, 
peck. 


42  Two  Years  Work  in  Numbers 

Exercise  42 

(1)  If  2  quarts  of  milk  cost  1  dime,  how  much 
milk  will  a  nickel  buy? 

(2)  Delmar  had  8  chickens  and  he  sold  2  of 
them.     He  now  has chickens. 

(3)  Charles  has  6  books  and  he  buys  2  more.  He 
then  has books. 

(4)  Genevieve  had  8  apples  and  she  gave  5  of 
them  to  her  playmates.    She  has apples  left. 

(5)  If  one  pencil  costs  2  cents,  4  pencils  will 
cost  — —  cents. 

(6)  I  have  8  pieces  of  crayon.  I  wish  to  give  2 
pieces  to  each  pupil.  To  how  many  pupils  will  I 
give  crayons  ? 

(7)  In  8  pints  there  are quarts.    In  8  gills 

there  are pints. 

Exercise  43 

1x1  =  1.  6x1  =  6. 

2x1  =  2.  2x3  =  6. 

3x1  =  3.  7x1  =  7. 

4x1  =  4.  8x1  =  8. 

2x2  =  4.  2x4  =  8. 

5x1  =  5.  4x2  =  8. 

8  less  4  are  4.  8  less  3  are . 

8-3  =  5.  8-5  =  . 


8-2  =  6.  8-6 


Tivo  Years  Work  in  Numbers 


43 


Change  each  of  the  addition  problems  to  two  sub- 
traction problems,  as: 


4 

8 

8 

5 

8 

8 

+4 

-4 

-A 

+3 

-5 

-3 

6 

8 

8 

7 

8 

8 

+2 

-6 

-2 

+1 

-7 

-1 

Copy  each  of  the  above  problems  5  times. 
Count  by  5  's  to  100.    Count  by  3  's  to  100. 

Exercise  44 

Count  by  10 's  to  100,  beginning  with  0,  1,  6,  5,  3, 

and  4. 
Take  the  combination  ^^6  and  2"  to  100,  as  shown 

below. 
Take  the  combination  ^^5  and  3"  to  100,  as  shown 

below. 


6  +  2—  8. 

5+  3  —  8, 

16  +  2  —  18. 

15  +  3  — 18. 

26  +  2  —  28. 

25  +  3  —  28, 

36  +  2  —  38. 

35  +  3  —  38. 

46  +  2  —  48. 

45  +  3  —  48. 

56  +  2  —  58. 

55  +  3  —  58, 

66  +  2  —  68. 

65  +  3  —  68, 

76  +  2  —  78. 

75  +  3  =  78, 

86  +  2  —  88. 

85  +  3  —  88, 

96  +  2  =  98. 

95  +  3  —  98, 

44  Two  YciO'.s  Worlx  in  Xionhers 

Take  these  combinations  to  100. 

3  +  4  =  7.  5  +  2  =  7,     .        4+4  =  8. 

Write:  7,  seven,  VII.         8,  eight,  VIII. 

Exercise  45 


How  many  feet  have  2  horses? 
How  many  feet  have  4  chickens? 
How  manv  ears  have  4  horses? 


2x2=? 
3x1=  ? 

4x2=  ? 

How  many  e^^es  have  2  people?  ^     ^  ^ 

How  many  hands  have  4  persons  ?  o     o q 

How  many  bills  have  8  birds  ?  o  .  I ? 

3  birds  have feet. 

2  chickens  have feet. 

2  horses  have feet. 

4  cows  have horns. 


Copy 


1x7=  ? 

3  +  3  =  ? 

2  +  5=? 

4  +  3  =  ? 
How  many  fingers  have  you  ?                       o     o ^j^ 

Count  from  eight  backwards.  ^     o ^ 

Name  8  kinds  of  trees. 


6  +  1 


2  times  4  are  8.  4  +  4  =  8.  8-4 

4  times  2  are  8.  5  +  3  =  8.  8-5 

8  times  1  are  8.  6  +  2  =  8.  8-6 

1  times  8  are  8.  7  +  1  =  8.  8-7 

Memorize  the  tables  given  above. 


Two  Years  Work  in  X umbers 


45 


Exercise  46 


Make  dominoes  like  these. 

5  cents  and  4  cents  are cents. 

6  books  and  3  books  are books. 

2  cats  and  4  cats  are cats. 


2  dots  and  7  dots  are 


dots. 


8  pencils  and  1  pencil  are 
Copy  three  times : 


pencils. 


4 

9 

9 

3 

9 

9 

+5 

-4 

-5 

+6 

-3 

-6 

9 

5 

4 

9 

6 

3 

8     ■ 

9 

9 

7 

9 

9 

+1 

-8 

-1 

+2 

-7 

-2 

9 

1 

8 

9 

2 

7 

46 


Two  Years  Work  iit  Sunibers 


Exercise  47 


Let  the  children  make  above  square,  using  inch 

squares. 

This  is  a inch  square. 

Each  side  is inches  long. 

Our  pencil  must  move inches  in  going  around 

this  square. 

There  are square  inches  in  this  square. 

3  times  3  square  inches  are  square  inches. 

3x3=? 
There  are threes  in  9.    One-third  of  9  is . 


Two-thirds  of  9  are .  Three-thirds  of  9  are 


Two  Years  Work  in  Numbers  47 

Exercise  48 

I  have  nine  squares  in  a  row. 

My  row  is  — —  inches  long  and inch  wide. 

I  put  them  in  three  rows.  * 

Now  I  have  a square. 

Each  row  is inches  long. 

One-third  of  9  square  inches  is square  inches. 

Copy  and  write  the  answer  to  each : 

3  threes  are  .  3x3=? 

3  times  3  are  .  9x1=? 

J  of  9  is  .  2x4=? 

f  of  9  are  .  3x2=? 

f  of  9  are  .  2x2  =  ? 

Draw  a  line  9  inches  long.  4        6.7 

Divide  it  into  thirds.  t^      t^      t^ 

Each  third  is inches  long. 

8        3        8 
Draw  another  line  9  inches  long.        ^^      ^g      _^ 

Divide  it  into  halves. 

Each  half  is inches  long.  9        9        9 

Measure  and  see  if  you  are  right.        ~4      -3      -2 


48  Two  Years  Work  in  Nwmhers 


Exercise  49 

Build  a  3-inch  cube. 

A  3-inch  cube  contains  — —  inch  cubes. 

Each  face  has square  inches. 

Each  edge  is inches. 

Each  face  has corners. 

Let  us  call  each  square  inch  one  square  foot. 

3x3  square  feet  are square  feet. 

9  square  feet  are square  yard. 

Show  by  drawing  on  the  blackboard. 

2x3  feet  are yards. 

1  square  foot  is of  a  square  yard. 

3  square  feet  are of  a  square  yard. 

Lay  rulers  to  show  a  square  yard. 

A  square  yard  contains square  feet. 

One-third  of  a  square  yard  is square  feet. 

Two-thirds  of  a  square  yard  are square  feet. 

Three-thirds  of  a  square  yard  are square  feet. 

Write  numbers  as  far  as  you  can. 


Two  Years  Work  in  Xumbers  49 

Exercise  50 

(1)  Gillette  has  4  marbles  and  James  has  5. 
They  both  have marbles. 

(2)  Elizabeth  had  3  dolls  and  her  playmates 
brought  6  more.    They  then  had dolls. 

(3)  If  3  pencils  cost  9  cents,  one  pencil  costs 
cents. 


¥ 


(4)  If  one  yard  of  ribbon  costs  3  cents,  3  yards 
will  cost cents. 

(5)  Mary  has  9  pears  and  she  gives  1  pear  to 
each  of  6  girls.    She  has pears  left. 

(6)  9  boys  form  a  solid  square.    There  are 

l)oys  in  each  row. 

(7)  4  girls  sit  in  each  of  2  rows  of  seats.    One 
sits  in  the  third  row.  How  many  girls  in  the  class  ? 

(8)  There  are  7  boys  at  the  blackboard  and  2 
boys  in  their  seats.    How  many  boys  in  class  ? 

Exercise  51 

Use  the  circle-maker. 

Make  9  circles  the  size  of  a  dollar. 

Make  9  circles  the  size  of  a  half  dollar. 

4 


50  Two  Years  Work  in  Xtunbers 

Make  9  circles  the  size  of  a  quarter. 

Measure  the  pieces  of  money  and  find  the  width  of 
each  piece. 

If  the  dollar  is  one  and  one-half  inches  wide,  place 
your  pencil  three-quarters  of  an  inch  from 
the  pin. 

Make  nine  circles,  color  them  and  place  them  on  a 
cardboard.  (Let  the  children  choose  the  size.) 


5  circles  and  4  circles  are 

3  circles  and  6  circles  are 

2  circles  and  7  circles  are 

9  circles  less  3  circles  are 

9  circles  less  5  circles  are 

9  circles  less  2  circles  are 


3 
_6 

8 

9 
-5 


1  nickel  is 
1  dime  is  - 
1  dime  is  - 


2  dimes  are 


cents.        1  pint  is 


cents, 
nickels. 
—  cents. 


1  bushel  is 


1  quart  is  - 
1  gallon  is 
1  peck  is  - 
pecks. 


gills. 

-  pints. 

-  quarts, 
quarts. 


Save  your  circle-maker  for  future  use. 


Two  Years  IVorJi  in  XtDubers  51 

Exercise  52 


OAJ^—gUOA^ 

^^^  a/m  — 

Copy  the  above  and  put  the  answer  in  each  blank 


52  Tico  Years  Work  tit  Xnmhers 


aAj2y  — 
/dt/?n£/  aJ  —  c^ritd. 


Copy  the  above  and  put  the  answer  in  each  blank. 


Two  Years  Work  in  Numbers  53 

Exercise  53 

REVIEW 

2  6  7  3  4  5  6  8 

+3        +1        +2        +3        +4        +4        +3        +1 


9    9 

6 

7 

8 

8 

9 

9 

-3   -7 

-3 

-2 

-5 

-6 

-2 

-8 

4    3 

6 

3 

5 

2 

1 

2 

x2    x3 

xl 

x2 

xl 

x2 

x6. 

x4 

i  of  4  is 

? 

i 

of  6 

—  ? 

4 

of  8  — 

? 

J  of  6  is 

? 

4 

of  9 

—  ? 

i 

of  8  — 

? 

Copy  the  above  and  place  answers.     Commit  to 
memory. 

Count  by  twos  to  50,  beginning  with  zero. 

Count  by  threes  to  50,  beginning  at  zero. 

Count  by  twos  to  50,  beginning  with  1. 

Count  baclavarcls  by  twos,  beginning  with  51. 


54 

/ 

Two  Years  Work  in  Numbers 
Exercise  54 

/r-n^         I 

5 

tAmr 

II 

d 

JJ7AJ2JZ^ 

III 

5 
b 

• 

¥ 
V 
VI 

7 

A£yQ/€my 

VII 

VIII 
IX 

10 

Tjz/yiy 

X 

Two  Years  Work  in  Numbers 


55 


Exercise  55 


10  dimes  make  a  dollar. 

1  dollar  is dimes. 

One-half  dollar  is dimes. 

5  dimes  and  5  dimes  are  — —  dimes. 

6  dimes  and  4  dimes  are dimes. 

7  dimes  and  3  dimes  are dimes. 

8  dimes  and  2  dimes  are dimes. 


One-half  of  10  dimes  is 
One-fifth  of  10  dimes  is 


—  dimes. 

—  dimes. 

Two-fifths  of  10  dimes  are dimes. 

Three-fifths  of  10  dimes  are dimes. 

Pour-fifths  of  10  dimes  are dimes. 

Let  children  make  paper  dimes  for  buying  and 
selling. 


56  Two  Years  Work  in  Numbers 

Exercise  56 

We  often  write  square  inches, — sq.  in. 
T  have  10  inch  squares  in  a  row. 

My  row  is long  and wide. 

I  place  my  inch  squares  in  two  equal  rows. 

I  have  an  oblong long  and wide. 

5  inch  squares  and inch  squares  are inch 

squares. 

Take  one  of  the  squares  from  the  lower  row  and 
place  it  in  the  upper  roAv. 

6  sq.  in  and sq.  in.  are  10  sq.  in. 

Place  another  square  above. 

7  sq.  in.  and sq.  in.  are sq.  in. 

Place  another  square  above. 

8  sq.  in.  and  2  sq.  in.  are sq.  in. 

Place  another  square  inch  above. 

9  sq.  in.  and  1  sq.  in.  are sq.  in. 

There  are pairs  of  numbers  that  make  ten. 

Note  : — ^Let  the  teacher  place  these  pairs  of  ten 
on  the  board  as  the  children  show  them  with  the 
squares. 


Two  Years  Work  in  Numbers 


57 


Exercise  57 


1  ten  is  10. 

2  tens  are  20. 

3  tens  are  

4  tens  are  

5  tens  are  

6  tens  are  

7  tens  are  

8  tens  are  

9  tens  are  

10  tens  are  


8  +  2=  ? 
6  +  4=  ? 

2x5=  ? 


Count  by  10,  beginning 
with  1 ;  with  2 ;  with  4. 


1 

11 
21 
31 
41 
51 
61 
71 
81 
91 
101 


Count  b}-  lO's  from  0  to  100  and  backwards. 
Count  bv  10 's  from  3  to  100  and  backwards. 


2 
12 
22 
32 
42 
52 
62 
72 
82 
92 
102 


Exercise  58 

^,  pairs  of  ten  are : 

5              4              3 

8 

9 

5              6              7 

2 

1 

10             10             10 

10 

10 

Take  your  inch  squares  and  show  each  pair. 

5  cents  and  5  cents  are cents. 

4  books  and  6  books  are books. 


58  Two  Years  Work  in  Numbers 

3  dogs  and  7  dogs  are  — —  dogs. 

8  birds  and  2  birds  are birds. 

9  horses  and  1  horse  are horses. 

2  stars  have points. 

2  nickels  are cents. 

2  hands  have fingers  and  thumbs. 

2  weeks  have school  days. 

10  dimes  make dollar. 

5  birds  have wings. 

5  persons  have eyes. 

5  chickens  have feet. 

Copy  the  pairs  of  10  five  times. 

Exercise  59 

Count  by  10 's  to  100,  beginning  with  0. 
Count  by  10 's  to  100,  beginning  with  5. 
Count  by  10 's  to  100,  beginning  wdth  6. 
Count  backwards  by  10 's  from  100  to  0. 
Count  backwards  by  10 's  from  109  to  9. 
Count  backwards  by  10 's  from  105  to  5. 

(1)  Eggs  are  10  cents  a  dozen.    5  cents  will  buy 
—  dozen. 

(2)  Milk  is  10  cents  a  half  gallon.    5  cents  will 
buy  a of  milk. 

(3)  At  20  cents  a  gallon,  1  dime  will  buy 

gallon. 

(4)  If  I  buy  ten  yards  of  ribbon  for  1  dollar,  one 
yard  costs . 


Two  Years  Work  in  Nttmbers  59 

(5)  At  10  cents  a  yard,  5  yards  will  cost  

cents. 

(6)  At  10  cents  apiece,  1  dollar  will  buy  

pencils. 

Write  the  numbers  to  50. 


Exercise  60 

I  have  5  pennies  and  a  5-cent  piece. 

^^Tien  I  count  my  money  I  find  I  have cents, 

or dime. 

10  cents  are  dime. 

5  cents  are of  a  dime. 

2  cents  are of  a  dime. 

2x5  cents  are  — —  cents,  or  — —  dime. 

One-half  of  a  nickel  is and cents. 

One-half  of  a  dime  is cents. 

One-fifth  of  a  dime  is cents. 

We  can  buv  with  a  nickel. 

We  can  buy  with  a  dime. 

We  can  buy    2  with. a  dime. 

We  can  buy  10  with  a  dime. 

We  can  buy    5  with  a  dime. 

Count  by  5's  and  10 's  to  100. 
Write  the  numbers  to  75. 


60  Two  Years  Work  in  Xumbers 


Exercise  61 

Change  each  of  the  following  addition  facts  to 
two  subtraction  facts,  as : 


5 

10 

10 

6 

10    10 

+5 

-5 

-5 

+4 

-6    -4 

10 

5 

5 

10 

4     6 

7 

10 

10 

8 

10     10 

+3 

-7 

-3 

+2 

-8    -2 

10 

3 

7 

10 

2     8 

9 

10 

10 

7  +  3  —  10. 

+1 

-9 

-1 

17  +  3  =  20. 

10 

1 

9 

27  +  3  —  30. 
37  +  3  —  40. 

Ar7          O       fA 

47  +  3  —  50. 

5  +  5: 

8  +  2: 

7  +  3: 

=  ? 

57  +  3  —  60. 
67  +  3  —  70. 

77  +  3  —  80. 

6  +  4 

—  1 

87  +  3  —  90. 

9  +  1 

? 

97  +  3  —  100, 

Count  by  5's,  4's  and  3's  to  100. 


Two  Year^  Work  in  Xtuubers  61 

Exercise  62 

A    DINNER    PARTY 

Use  your  circle-maker  and  make  some  paper  plates. 

Measure  your  dinner  plates  at  home. 

Make  your  plates  the  size  of  them  if  your  circle- 
maker  is  long  enough. 

Measure  your  pie  plates  and  make  one. 

Measure  your  saucers  and  make  one. 

If  3^ou  wish,  make  a  cup. 

Measure  your  sauce  dishes  and  make  one. 

Now,  set  your  table. 

How  many  people  will  you  have  at  your  table  ? 

How  many  on  a  side  ?    On  the  end  ? 

How  many  on  two  sides  ?    On  two  ends  ? 

Name  4  kinds  of  meat ;  2  kinds  of  bread. 

Name  4  kinds  of  fruit ;  4  kinds  of  pies. 

Name  2  kinds  of  pickles. 

What  will  you  have  for  dessert  ? 

How  many  spoons  will  you  need  at  each  place  ? 

How  many  spoons  for  all  ? 

How  many  knives  and  forks  for  all  ? 


62  Two  Years  Work  in  X umbers 

Exercise  63 

(1)  If  1  yard  of  ribbon  costs  2  cents,  5  yards  will 
cost cents. 

(2)  I  have  a  dime.  I  buy  5  pencils  with  it. 
What  do  I  pay  for  each  pencil  ? 

(3)  If  1  quart  of  milk  costs  5  cents,  one-half 
gallon  costs cents. 

(4)  In  going  to  school  I  rode  8  blocks  on  the  car 
and  walked  2  blocks.  How  far  is  my  home  from 
school  ? 

(5)  I  buy  8  cents  worth  of  drawing  paper.  I 
hand  the  merchant  I  dime.  How  much  change  will 
he  give  me  ? 

(6)  I  buy  2  yards  of  ribbon  at  4  cents  a  yard.    I 

hand  the  saleslady  a  dime.     She  gives  me  

cents  in  change. 

(7)  If  I  buy  2  pencils  at  5  cents  apiece,  how 
much  change  will  I  get  from  a  dime  ? 

(8)  At  10  cents  a  yard,  how  many  yards  can  I 
buy  for  1  dollar? 


Two  Years  Work  in  Nu7nbers 


63 


Exercise  64 


1  dollar 
1  dime 
1  nickel 
1  quart 
1  gallon 


1  pint 
1  peck 
1  bushel 
1  yard 
1  foot 


2  dollars  are 
2  dimes  are  - 


dimes. 


4  nickels  are 
2  quarts  are  - 
2  gallons  are 
2  pints  are  — 

2  bushels  are 

3  yards  are  — 


—  cents. 

—  cents. 

—  pints. 

—  quarts, 
gills. 

—  pecks. 
■  feet. 


2x2  = 
2x3  = 
5x1  = 
3x3  = 

2x5  = 
4x2  = 
6x1  = 

7x]  = 


One-half  peck  is  - 

One-half  foot  is  — 

One-half  gallon  is 

One-half  gallon  is 

One-half  dollar  is 


—  quarts, 
inches. 

—  quarts, 

—  pints. 

—  cents. 


Copy  this  page  with  correct  answers. 


G4  Two  Years  Work  hi  Xmnhers 

Exercise  65 

^^  A  pint  is  a  pound  the  world  around,"  they  say. 
A  pint  fills  2  teacups.  1  teacupf  ul  is pound. 

(1)  We  have  6  windows  and  2  doors  in  our  room. 
We  have more  windows  than  doors. 

(2)  I  bought  a  peck  of  cherries  and  sold  4  quarts. 
I  have quarts  left. 

(3)  I  bought  a  gallon  of  milk  and  gave  2  quarts 
to  my  friend.    I  had quarts  to  use. 

(4)  The  milkman  brought  us  10  quarts  of  milk. 
We  had gallons  and quarts. 

(5)  I  ordered  2  gallons  of  vinegar.    How  many 
quart  jars  will  it  fill? 

(6)  Sugar  is   5   cents   a   pound.     How   many 
pounds  can  I  get  for  a  dime  ? 

(7)  We  shall  use  3  pounds  of  sugar  for  our 
candy.    How  many  teacupf uls  shall  we  use  ? 

Write  the  pairs  of  10,  9,  8,  7. 

Exercise  66 

DRILL 


1 

3 

6 

4           7 

5 

2 

8 

+2 

6 

3 

1 

5           2 

4 

7 

8 

+3 

10 

8 

5 

7           9 

6 

4 

3 

T^vo  Years  Work  in  Numbers 


65 


8 

10 

6 

9           7 

5 

3 

4 

. 

-2 

10 

8 

6 

9 

7 

5 

4 

-4 

Write  the  pairs  of  the  numbers : 

9,  10,  8,  7,  5,  4,  3,  6. 
Count  by  fives,  beginning  with  0. 

Exercise  67 

Pint  may  be  written,  pt. 
Quart  may  be  written,  qt. 
Peck  may  be  written,  pk. 
Bushel  may  be  written,  bu. 

2  times  4  pints  are  qt. 

3  times  3  pints  are  qt.  and  - 

2  times  5  quarts  are  pk.  and 

4  times  2  gills  are pt. 

10  quarts  are  pints. 

10  gills  are pints  and . 

10  quarts  are  — 
10  pints  are  — 

9  pints  are  — 

7  pints  are  — 

6  pints  are  — 

5  quarts  are  — 

6  quarts  are 


over, 
over. 


gallons  and 
quarts, 
quarts  and 
quarts  and 
quarts. 
-  gallon  and 
■  gallon  and 


over, 
over. 

over, 
over. 


Copy  this  exercise  and  fill  blanks. 


66  Two  Years  Worh  in  Niimhers 


Exercise  68 


TEST 


1x1  — 

2  +  2 

2x1  — 

1  +  9 

3x1  — 

7  +  3 

2x2  — 

8  +  2 

4x1  — 

9-3 

5x1  — 

5-4 

2x3  — 

6-4 

6x1  — 

7  +  2 

7x1  — 

8  +  1 

8x1  — 

9-8 

4x2  — 

5  +  5 

9x1  — 

10-5 

3x3  — 

6  +  4 

2x5  — 

8-8 

0x1  — 

10-9 

5x2  — 

10-6 

3  +  4 
7  +  1 
8-2 
9  +  1 
8-3 
5-3 
7-4 
8-3 
9-5 
5-3 
6-4 
9-7 

10-8 
9-2 

10-8 
9-9 


Copy  and  recite  the  above  facts. 


PART  TWO 


TO  THE  TEACHER 

Review  the  number  facts  studied  in  Part  One. 
If  necessary,  continue  to  use  objects  to  develop 
these  facts.  Developing,  reviewing  and  drilling 
will  produce  the  desired  result.  Seeing,  imaging, 
thinking  and  memorizing  constitute  the  process  of 
number  learning. 


Two  Years  Work  in  Nimihers 


69 


Exercise  1 


10  units  make  one  ten. 

10  tens  make  one  hundred. 


We  can  tell  Avhether  a  figure  stands  for  units  or 
for  tens  by  the  place  it  occupies. 


10 


C 


I 

D 


10  IS  ten  times  i. 


tJ2/n  /ym 

11  is  made  of 
1  ten  and  1. 

11  is  11  times  1. 

10  cents  make   a  dime. 


10 
II 


10 

10 

10 

10 

10 

10 

10 

10 

10 

10 

10 
100 

10  dimes  make  a  dollar 


11  cents  make  a  dime  and  1  cent. 


70  Two  Years  Work  in  Numbers 

Exercise  2 

Use  inch  squares  for  the  work  that  follows : 

I  have  11  inch  squares  in  a  row. 

My  row  is inches  long  and inch  wide. 

I  move  2  inch  squares  below.    I  find  that  2  inch 

squares  and  inch  squares  are  11  inch 

squares. 
I  move  4  inch  squares  below.     I  find  that  6  inch 

squares  and  inch  squares  are  11  inch 

squares. 
I  place  3  inch  squares  back  in  the  upper  row.  I  now 

find  that  8  inch  squares  and inch  squares 

are  11  inch  squares. 
I  move  1  more  inch  square  below.    Now  what  num- 
bers do  I  find  make  11  ? 
(Let  the  teacher  copy  these  pairs  of  numbers  on  the 

board  as  the   children  w^ork  them  out  ■  with 

squares.) 

Exercise  3 
The  pairs  of  numbers  that  make  11  are : 

5  9  7  8  10 

6  A  A  —  J: 
11             n             11             11  11 

Copy  the  above  combinations  five  times. 

6  pears  and  5  pears  are pears. 

7  pecks  and  2  pecks  are pecks. 

8  apples  and apples  are  11  apples. 


Two  Years  Work  in  Numbers  71 

1  box  and boxes  are  11  boxes. 

3  dogs  and  8  dogs  are dogs. 

5  pigs  and pigs  are  11  pigs. 

4  girls  and girls  are  11  girls. 

11  boys  less  4  boys  are boys. 

11  books  less  8  books  are books. 

11  knives  less  3  knives  are knives. 

Write: 


Exercise  4 

If  necessary,  use  drawings  on  the  blackboard  to 
work  out  the  following  problems : 

In  11  pecks  there  are bushels. 

In  11  pints  there  are quarts. 

In  11  quarts  there  are gallons. 

In  11  gills  there  are pints. 

In  11  feet  there  are yards. 

11  things  are things  and things. 

11  boxes  are boxes  and boxes. 

11  books  are books  and books. 

11  houses  are  4  houses  and houses.    ' 

(1)  There  are  3  houses  on  one  street  and  8 

houses  on  another.    On  both  streets  there  are 

houses. 


72  Two  Years  Work  in  Numhers 

Exercise  5 

Let  each  child  use  inch  squares  and  work  out  the 
five  pairs  of  numbers  that  make  11.  White  the  ad- 
dition combinations  that  make  the  number  11  and 
change  each  combination  to  two  subtraction  prob- 
lems, as  follows : 


5 

11 

11 

7 

11 

11 

+6 

-5 

-6 

+4 

-A 

-7 

11 

6 

5 

11 

7 

4 

8 

11 

11 

9 

11 

11 

+3 

-8 

-3 

+2 

-9 

-2 

11 

3 

8 

11 

2 

9 

10 

11 

11 

10 

11 

10 

+1 

-10 

-1 

-4 

-7 

-8 

11 

1 

10 

6 

4 

2 

(1)  A  boy  had  10  rabbits,  but  4  ran  away.    He 
had left. 

(2)  Edith  had  3  dolls  and  her  aunt  gave  her  4 
more.    She  then  had dolls. 

(3  Dorothy  had  6  little  cups  and  broke  4.     She 
bought  2  more.    How  many  had  she  then  ? 


Two  Years  Worh  in  Niimhers  73 

Exercise  6 


Let  the  children  make  3  dominoes 
of  each  kind. 

Write  pairs  of  11  in  figures  from 
dots  on  dominoes. 

Change  each  addition  problem  to 
two  subtraction  problems. 


Let  children  keep  these  dominoes  to  use  in  their 
game  of  buying  and  selling. 

Exercise  7 

(1)  There  are  7  birds  on  the  grass  and  4  birds 
on  the  porch.    In  both  places  there  are birds. 

(2)  I  bought  9  cents  worth  of  paper  and  a  two- 
cent  postage  stamp.    How  much  did  I  spend  ? 

(3)  I  paid  5  cents  for  colored  crayons,  3  cents 
for  pencils  and  3  cents  for  paper.  How  much  did 
I  spend  ? 


74  Two  Years  Work  in  Numbers 

(4)  My  father  gave  me  11  cents  and  I  paid  a 
dime  for  two  pencils.  How  many  cents  have  I  now  ? 

(5)  Henry  had  11  cents.  He  bought  a  pencil  for 
5  cents ;  a  post  card  for  3  cents.  How  much  has  he 
now? 

(6)  A  farmer  has  11  horseshoes.  He  can  shoe 
horses  and  have shoes  left. 

(7)  A  lady  has  11  gloves.    She  has pairs  of 

gloves  and glove. 

Exercise  8 

Use  toy  money  to  work  out  these  problems.  Let 
children  make  paper  circles  the  size  of  the  different 
pieces  of  money  used. 

In  11  cents  there  are nickels  and cent. 

In  11  cents  there  are dime  and cent. 

In  3 1  cents  there  are  3-cent  pieces  and 

cents. 

In  10  cents  there  are nickels. 

In  1  dollar  there  are dimes. 

In  1  dime  there  are cents. 

In  2  dimes  there  are  cents. 

In  3  dimes  there  are  cents. 

In  2  dimes  there  are  nickels. 

In  5  dimes  there  are  — —  nickels. 

In  2  dollars  there  are  dimes. 

In  5  dollars  there  are  dimes. 

In  one-half  dollar  there  are nickels. 

In  15  cents  there  are dime  and nickel. 


Two  Years  Work  in  Numbers  75 

Exercise  9 

11  is  ?  more  than  3.  11  is  ?  more  than  6. 

11  is  ?  more  than  9.  11  is  ?  more  than  2. 

11  is  ?  more  than  4.  11  is  ?  more  than  7. 

11  is  ?  more  than  5.  11  is  ?  more  than  8. 

There  are  2  fives  and  ?  in  11. 
There  are  3  threes  and  ?  in  11. 
There  are  2  fours  and  ?  in  11. 
There  are  3  twos  and  ?  in  11. 


10  is  1  less  than  ? 
9  is  2  less  than  ? 
7  is  4  less  than  ? 

3      8      5      6 
3      2      3      4 

5 
6 

6      5 

2      5 

6  is  5  less  than  f 
4  is  2  less  than  ? 
8  is  3  less  than  ? 

3  5       3      4 

4  4      6      7 

Exercise  10 

Copy  and  solve  the  problems  given  below.    Use 
them  for  rapid  oral  work  during  the  recitation. 


6 

7 

3 

5 

8 

6 

9 

+3 

+2 

+3 

+1 

+3 

+1 

-1 

9 

9 

6 

6 

11 

7 

10 

-3 

-7 

-3 

-5 

-8 

-6 

-9 

3 

6 

4 

2 

3 

2 

5^ 

x2 

xl 

x2 

x2 

x3 

x5 

x2 

76  Two  Years  Work  in  Nunihers 


3 

7 

2 

6 

2 

1 

2 

1 

5 

1 

3 

2 

1 

6 

1 

7 

2 

1 

2 

2 

8 

2 

3 

2 

3 

4 

1 

1 

2 

1 

4 

1 

3 

3 

3 

2 

In  what  month  does  Thanksgiving  come  ? 
Name  11  things  for  which  we  should  be  thankful. 

Exercise  11 

(1)  I  have  a  dime  and  1  cent. 

(2)  I  have cents. 

(3)  I  can  buy  with  11  cents. 

(4)  I  can  buy  with  11  cents     and    have 

cent  left. 

(5)  I  can  buy with  11  cents  and  have 

cents  left. 

(6)  I  can  buy  3  with  11  cents  and  have 

cents  left. 


(7)  5  apples  at  2  cents  apiece  cost . 

(8)  3  oranges  at  2  cents  apiece  cost cents. 

If  I  give  the  clerk  10  cents,  I'll  get cents  in 

change. 

(9)  If  I  buy  4  cards  at  2^  cents  apiece,  how 
many  cents  must  I  give  the  salesman  ? 

(10)  With  11  cents  I  can  buy  a  5-cent  tablet  and 
have cents  left. 


Tivo  Years  Worh  in  Numbers 


77 


Exercise  12 


Exercise  13 


11  less  2  times  3  are 
11  less  7  times  1  are 
11  less  2  times  4  are 
11  is  5  times  2  and  - 
11  is  4  times  1  and  - 
11  is  6  times  1  and- 
11  is  2  times  3  and  - 
11  is  3  times  3  and  - 


11 
-4 

11 
-5 

11 

-8 


In  five  and  one-half  inches  there  are 

half  inches. 

One-half  foot  and inches  are  11 

inches. 
One-half  dozen  and  2  eggs  are  

eggs. 
11  half  inches  are inches. 

8  half  inches  are inches. 

10  half  inches  are inches. 

9  half  inches  are inches. 

7  half  inches  are inches. 

6  half  inches  are inches. 

11  pints  are  quarts  and  

pint. 

11  quarts  are  peck  and  

quarts. 


11 

-6 

11 
-3 

11 
-2 


78  Two  Years  Work  in  Numbers 

8  +  3  =  11.  Take  the  following  com- 

18  +  3  =  21.  binations  to  100 : 


28  +  3  =  31. 
38  +  3  =  41. 


9  +  2  =  11. 
7  +  4  =  11. 


48  +  3  =  51.  6  +  5  =  11. 

58  +  3  =  61.  10  +  1  =  11. 

68  +  3  =  71.  

78  +  3  =  81.  .  3  +  5  +  2  =  ? 

88  +  3  =  91.  6  +  4  +  1  =  ? 

98  +  3  =  101.  1  +  8  +  2  =  ? 


Exercise  14 

(1)  Thomas  goes  to  school  5  days  in  one  week. 
In  two  weeks  he  goes days. 

(2)  John  lives  6  blocks  on  one  side  of  the  school- 
house.  Reynolds  lives  5  blocks  on  the  other  side. 
The  boys  live blocks  apart. 

(3)  Mother  gave  me  5  cents  on  Monday  and  4 
cents  on  Tuesda}^    I  now  have cents. 

(4)  Willie  picked  7  boxes  of  berries  in  the 
morning  and  4  boxes  in  the  afternoon.  He  picked 
boxes  of  berries  during  the  day. 

(5)  The  telephone  rang  8  times  in  the  morning 

and  3  times  in  the  afternoon.    It  rang times 

during  the  day. 

(6)  On  Arbor  day  the  children  planted  11  trees 
but  3  of  them  died.    — —  trees  are  growing. 

Copy  the  pairs  of  the  numbers    9,     10,     11. 


Two  Years  Work  in  Numbers 


79 


Exercise  15 

5 

■^      A       f^ 

Add  2  to  each  numbei' 

3/\2 

around     the     diamond. 

7       \ 

Then  add  3.  Then  add  4. 

/                  \ 

Subtract  2  from  the 

numbers     around 

the 

Y         Adds.     \6 

square.  Then  subtract  4. 
7       Q        il       6 

K        A^ 

10 

\     /3      10 

6 

7\A          ^ 
5             ^ 

Draw  similar  fig- 
ures    on    the    board, 

Subtract 
3 

8 
9 

and  give  rapid  drills    ^ 

10 

on  the  fundamental 

8      11        9 

7 

number  facts. 

Write  the  pairs  of  8,  9, 10, 11  and  change  each  ad- 
dition problem  to  2  subtraction  problems. 

Exercise  16 

How  many  horses  can  be  shod  Avitli  ten  shoes  ? 
How  many  pairs  of  gloves  in  10  gloves? 
How  many  pairs  of  hose  in  11  hose? 
How  many  pints  in  8  gills? 
How  many  quarts  in  10  pints  ? 
How  many  school  weeks  in  10  days  ? 
How  many  dimes  in  2  dollars? 


80  Two  Years  Work  in  Numbers 

How  many  cents  in  2  dimes  ? 
How  many  bushels  in  11  pecks? 
How  many  bushels  in    8  pecks? 
How  many  pecks  in  2  bushels  ? 
How  many  pints  in  4  quarts  ? 
How  many  quarts  in  2  gallons  ? 
How  many  nickels  in  20  cents  ? 
How  many  yards  in  11  feet? 
How  many  gills  in  2  pints  ? 


Exercise  17 

Copy  and  memorize  the  following : 

2x1  — 

3  +  4  — 

6  +  5  — 

3x2  — 

7  +  3  — 

8-4  = 

7x1  = 

8  +  2  — 

9-2  — 

2x5  — 

9  +  1  = 

11-9  — 

6x1  — 

6  +  3  — 

10-5  — 

3x3  — 

9-3- 

6  +  5  — 

4x2  — 

10-7  — 

5  +  5  — 

.     -     8x1  — 

11-5  — 

10-5  — 

9  +  1  = 

3  +  8  — 

6-4  — 

10  x  1  — 

7  +  4  — 

8-7  — 

11  X  1  — 

3  +  3  — 

11  -  7  — 

ConntbylO's 

to  100. 

i  of  2,  4,  6,  8, 10, 

Count  by  11 's 

to  100. 

1 

of  3,  6, 9, 30. 

Write  the  following : 

Two  Years  Work  in  Numhers 


81 


Exercise  18 


This  rectangle  is 

It  is inches  wide. 


inches  long. 


There  are 
There  are 


square  inches  in  each  row. 
rows  of  square  inches. 


Count  the  square  inches. 

We  find  there  are square  inches  in  a  rectangle 

inches  long  and inches  wide. 


Our  pencil  will  travel 
this  rectangle. 


inches  in  going  around 


82 


Two  Years  Work  in  Numbers 


Exercise  19. 

Use  inch  squares  in  developing  the  following : 
I  have  12  inch  squares  in  a  row. 
My  row  is  inches  long  and  inch  wide. 

My  row  contains square  inches. 

I  place  6  of  these  inch  squares  below. 

I  now  have  a  rectangle inches  long  and 

inches  wide. 

My  rectangle  is foot  long. 

My  pencil  will  travel inches  in  going  around 

this  rectangle. 
One-half  of  12  square  inches  is  - 
One-sixth  of  12  square  inches  is 

With  the  squares  show  that 

6  5  8  9 

^  _7  _4  _3 

12  12  12  12 


square  inches, 
square  inches. 


10 
_2 
12 


11 
12 


Exercise  20 

12  things  make  a  dozen. 

We  buy by  the  dozen. 

One-half  of  a  dozen  oranges  is ^  oranges. 

One-half  of  a  dozen  eggs  is eggs. 

6  lemons  are dozen  lemons. 

6  apples  are dozen  apples. 

inches  make  a  foot. 

One-half  foot  is inches. 

months  make  a  year. 


Tivo  Years  Worh  in  Numbers 


83 


One-half  year  is months. 

3  months  and  3  months  make  — 

4  eggs  and  2  eggs  make 

4  oranges  and  8  oranges  make  - 

5  apples  and  7  apples  make  a  - 
7  months  and  5  months  make  a 
4  inches  and  8  inches  make  a  - 


year 


dozen. 
-  dozen. 


Exercise  21 


We  buy  and  sell 
eggs  by  the  dozen. 

How  many  eggs  in  the 
nest? 

We  use  eggs  to  


Where  does  the  gro- 
cer get  the  eggs  ? 

Did  you  ever  hunt  eggs?    Did  you  find  a  dozen? 
How  many  eggs  did  you  find  ? 
We  want  to  buy  and  sell  eggs  to-morrow. 
We  will  cut  eggs  like  the  picture  out  of  thick  paper. 
Each  pupil  may  make  a  dozen  paper  eggs.     Use 
this  pattern. 


84  Two  Years  Work  in  Ntimhers 

Exercise  22 

This  game  is  store-keeping. 

We  shall  buy  and  sell  eggs. 

We  shall  use  the  one-cent  pieces  that  we  have  made 

for  our  pennies. 
James  may  be  banker. 
We  shall  use  our  dominoes  for  checks  with  which 

to  draAv  money  from  the  bank. 
Thomas  will  be  grocer. 
To-day  we  can  get  eggs  for  1  cent  apiece. 

^^I  want  ten  eggs.    I  shall  give  you cents." 

^^I  want  one-half  dozen  eggs.    I  shall  give  you 

cents." 
^^I  want  one  dozen  eggs.     I  shall  give  you 

cents." 
^^I  want  two  dozen  eggs.     I  shall  give  you  

cents." 


Exercise  23 

Let  us  use  12  inch  cubes. 
I  place  them  in  a  row. 
I  see  2  times  12  faces. 

Each  face  has corners  and sides. 

I  place  the  cubes  in  2  equal  rows. 

In  two  rows,  they  are inches  long, inches 

wide,  and inch  high. 


Two  Years  Work  in  Numbers  85 

In  3  rows,  they  are inches  long, inches 

wide,  and inch  high. 

When  we  place  the  cubes  in  2  rows  we  find  that  one- 
half  of  12  is  6.    One-sixth  of  12  is  2. 

When  we  place  them  in  4  rows,  we  find  that  one- 
fourth  of  12  is  3. 

When  we  place  them  in  3  rows,  we  find  that  one- 
third  of  12  is  4. 

Copy  the  following : 

i  of  12  is  6.  I  of  12  is  4. 

i  of  12  is  3.  1  of  12  is  2. 

Exercise  24 
Use  inch  squares  to  show  the  following : 
Make  a  rectangle  4  inches  long  and  3  inches  wide. 

We  must  take  our  3  inch  squares  4  times  to  make 
12  inch  squares. 
4  times  3  are  12.  4x3  =  12. 

We  must  take  our  4  inch  squares  3  times  to  make 
12  inch  squares. 
3  times  4  are  12.  3x4  =  12. 

Make  a  rectangle  2  inches  by  6  inches. 

We  must  take  our  6  square  inches  2  times  to  make 
12  square  inches. 

2  times  6  are  12.  2x6  =  12. 


86  Ttvo  Years  Work  in  Numbers 

We  must  take  our  2  square  inches  6  times  to  make 
12  square  inches. 

6  times  2  are  12.  6x2  =  12. 

Exercise  25 

Use  12  inch  squares  for  the  work  below. 

We  find  we  can  separate  12  things  into  2  parts. 

In  each  part  there  are  6  things. 

We  may  say  this  as  follows : 

12  things  divided  by  2  are  6  things. 

12  things  -^-  2    =    6  things. 

12  things  divided  by  6  are  2  things. 

12  things         -f-         6    =    2  things. 

Now  place  the  inch  squares  in  3  rows. 

12  things  divided  by  3  are  4  things. 

12  things         -V-  3    =    4  things. 

12  things  divided  by  4  are  3  things. 

12  things         -T-         4   =    3  things. 

One-third  is  one  of  three  equal  parts. 

One-third  of  12  is  4. 

One-fourth  is  one  of  4  equal  parts. 

One-fourth  of  12  is  3. 

One-sixth  is  one  of  6  equal  parts. 


Two  Years  Work  in  Numbers  87 

Exercise  26 


Can  you  tell  the  time  of  day  ? 

What  helps  to  tell  us  the  time  of  day? 

How  many  hours  does  the  face  of  the  clock  repre- 
sent? 

To  what  number  does  this  long  hand  point  ? 

The  long  hand  always  points  to  12  when  the  clock 
strikes  the  hour. 

Where  is  the  short  hand  ?    What  time  is  it  ? 

At  what  time  did  you  come  to  school  ? 

Exercise  27 

Use  the  clock  face  in  Exercise  26  for  the  following : 

The  short  hand  tells  the  hour. 

The  long  hand  tells  the  minutes  before  or  after  the 

hour. 
What  part  of  the  hour  has  passed  when  the  minute 

hand  is  at  VI? 


88  Tivo  Years  Work  in  Numbers 

When  the  minute  hand  is  at  III? 
When  the  minute  hand  is  at  IX? 
How  many  minute  spaces  between  XII  and  I? 

Between  XII  and  II?  Between  II  and  IIII? 

Between  VII  and  IX? 

One-fourth  of  12  hours  is hours. 

One-third  of  12  hours  is hours. 

One-half  of  12  hours  is hours. 

There  are  60  minutes  in  one  hour. 

Show  by  the  clock  face  how  many  minutes  in  a 

half  hour. 
In  a  quarter  of  an  hour  there  are minutes. 

Exercise  28 

TEST 

1x1=  7x1=  2x6  = 

2x1=  2x4=  3x4  = 

3x1=  8x1=  12x1  = 

2x4=  3x3=  2x7  = 

1x4=  9x1=  7x2  = 

5x1=  2x5=  3x5  = 

6x1=  10x1=  5x3  = 

2x3=  11x1  = 

1  of    4  is .  1  of  10  is . 

1  of    6  is .  ^  of  12  is . 

J  of    9  is .  1  of  12  is . 

1  of    8  is .  1  of  15  is . 

Copy  and  memorize  these  number  facts. 


Two  Years  Work  in  Numbers  89 

Exercise  29 

(1)  If  you  buy  a  dozen  lemons,  how  many  will 
you  get?  Put  one-half  of  them  in  a  dish.  How 
many  are  left  ? 

(2)  How  many  working  days  in  2  weeks  % 

(3)  6  two-cent  stamps  cost cents. 

(4)  It  takes cents  to  buy  6  two-cent  stamps. 

(5)  How  much  will  it  cost  to  stamp  5  letters'? 

(6)  Delmar  bought  a  dozen  oranges;  he  gave  3 
to  his  brother,  3  to  his  friend,  and  ate  3.  He  still 
has oranges? 

(7)  Place  12  squares  in  groups  of  3. 

(8)  How  many  horses  will  12  shoes  shoe  ? 

(9)  James  is  out  of  school  during  June,  July 
and  August.    How  many  months  is  he  in  school  ? 

(10)  How  many  months  in  one-third  of  a  year  ? 

Exercise  30 

How  many  months  in  a  year  ? 

How  many  seasons  in  a  year? 

How  many  months  in  each  season  ? 

Name  the  seasons  and  the  months  in  each  season. 

How  many  feet  have  3  horses? 

How  many  horns  have  6  cows  ? 

How  many  points  have  4  triangles  ? 

How  many  corners  have  3  squares  ? 

How  many  legs  have  3  tables  ? 

How  many  inches  in  a  foot? 


90  Two  Years  Work  in  Numbers 

How  many  inches  in  one-half  of  a  foot  ? 

How  many  inches  in  one- third  of  a  foot  ? 

How  many  inches  in  two-thirds  of  a  foot  ? 

How  many  inches  in  one-fourth  of  a  foot  ? 

How^  many  inches  in  two-fourths  of  a  foot  ? 

Write  pairs  of  the  numbers  12,  11,  10,  9,  8, 

Exercise  31 

Make    concrete   problems   using   the   following 
combinations : 


2 

6 

8 

7 

8 

3 

+4 

+4 

+2 

+4 

+3 

+9 

9 

11 

10 

9 

12 

12 

-2 

-4 

-8 

-4 

-8 

-7 

4 

5 

3 

2 

4 

6 

x2 

x2 

x3 

x3 

x3 

x2 

(1 )  2  girls  on  one  bench  and  4  girls  on  another. 
2  +  4  = . 

(2)  If  nine  birds  were  on  the  fence  and  2  flew 
away, birds  were  left  on  the  fence.    9  -  2  = 

(3)  A  boy  cut  2  apples  into  quarters.    2  x  ?  ==  8 
quarters. 


Two  Years  Work  in  Numbers  91 


Exercise  32 


TEST 


1x1  — 

12-4-- 

12  :  4  — 

2x1  — 

11-3  = 

12  :  6- 

3x1  — 

9  +  2  — 

10  :  2  = 

2x2  — 

12-5  — 

9:3  — 

4x1  — 

6  +  5  — 

12  :  3  — 

5x1— ~ 

8  +  4  — 

10  :  5  — 

6x1  = 

7  +  3  — 

8  :  4  — 

2x3  — 

12  -  7  — 

12  :  2  — 

7x1  — 

11-6  — 

12  :  6  = 

8x1  — 

10-4  = 

10  :  10  = 

2x4  — 

8  +  2  — 

9  --  9  — 

9x1  — 

12-6  — 

4  :  2  — 

3x3  = 

12-8  — 

3:1- 

10x1  — 

11-4  — 

5   :   5  = 

2x5  — 

9  +  6  — 

6   :   3  — 

11x1  — 

12-9  — 

7:7  = 

12x1  — 

11-5  — 

8  :  8  — 

3x4  — 

10-7  — 

2^-1  — 

6x2  — 

10-8  — 

4  :  4  — 

92 


Tivo  Years  Work  in  Numhers 


Exercise  33 


(Use  a  United  States  flag  for  this  exercise.) 


Count  the  red  stripes  in  the  flag. 

Count  the  white  stripes. 

stripes  and stripes  are 


stripes. 


If  one  red  stripe  were  torn  away,  there  would  be  an 
equal  number  of  each.  How  many  of  each 
kind  ?    How  many  of  both  kinds  ? 

13  stripes  are  how  many  more  than  12  stripes  ? 

How  many  red  stripes  below  the  blue  field  ? 

How  many  red  stripes  to  the  left  of  the  blue  field  ? 

Oklahoma  is  the  last  star  in  the  flag.  What  num- 
ber is  her  star  ? 


Tivo  Years  Work  in  Niimhers  93 

Exercise  34 

13  is  1  ten  and  3  ones  or  units. 
The  pairs  of  13  are : 

6  8  9        10        11        12 

J7        ^        _4        ^        _2        _1 
13        13        13        13        13        13 

Show   the   above    combinations   with   the    inch 
squares. 

How  many  pairs  of  numbers  make  13  ?    Why  ? 
How  many  more  are  13  books  than  12  books  ? 
Count  to  13  by  I's. 

Count  to  13  by  2's.  3        2        1 

Count  to  13  by  3's.  2        2        2 

How  many  4 's  in  13?  5        2        1 

How  many  5 's  in  13?  4        2        2 

How  many  feet  in  13  inches?  12         1 

How  many  pecks  in  13  quarts  ? 

Copy  and  memorize  the  pairs  of  numbers  that 
make  13. 

Exercise  35 

Name  the  odd  numbers  to  13. 

All  numbers  that  may  be  divided  by  2  without  a 

remainder  are  called  even  numbers. 
Name  the  even  numbers  to  100. 


94 


Two  Years  Work  in  Numbers 


Name  the  even  numbers  from  100  to  0. 

Try  to  place  13  inch  squares  in  two  equal  rows. 

What  do  you  discover? 


13  cents  less  1  dime  are 


cents. 
-  cents. 


13  cents  less  1  nickel  are  — 
13  inches  less  1  foot  is  — - —  inch. 

13  quarts  less  1  gallon  are quarts. 

13  quarts  less  4  quarts  are pints. 


13  dimes  less  1  dollar  are 


dimes. 

-  egg. 

-  pecks. 


13  eggs  less  1  dozen  eggs  is  — 
13  pecks  less  2  bushels  are  — 

13  quarts  less  1  peck  are quarts. 

13  gills  less  5  gills  are pints. 


Write:     cents,  dimes,  nickels,  quarts. 


13  is  4  more  than  ? 
13  is  9  more  than  ? 
13  is  5  more  than  ? 
13  is  3  more  than  ? 


Exercise  36 


13  is  2  more  than  ? 
13  is  7  more  than  ? 
13  is  6  more  than  ? 
13  is  11  more  than  ? 


2  +  3  +  ?  —  13 

4  +  5  +  !  —  13 

3  +  4+?—  13 

4  +  6+  ?—  13 

2  +  7+?—  13 

5  +  3  +  ?  —  13 

3  +  3  +  ?  —  13 

6  +  5  +  ?  =  13 

-     Two  Years  Work  ui  Nunihers  95 

2+2+2+2+2+2+1=  ?         1  3  4      ' 2 

3  +  3  +  3  +  3  +  1=   ?  2  4  5        1 

4  +  4  +  4  +  1=  ?  3  5  2        3 

5  +  5  +  3=?  8  2  15 

6  +  6  +  1=  ?  A  i.  1.      A 

Find  J  of  each  of  the  following  numbers: 
2,4,5,6,7,8,9,10,11,12. 

Exercise  37 

(1)  If  George  had  13  trees  and  tried  to  set  them 
in  2  rows,  he  would  liave  to  set  7  trees  in  one  row 
and trees  in  the  other. 

(2)  13  birds  in  the  tree.     9  flew  away.     

birds  were  still  in  the  tree. 

(3)  What  is  the  largest  piece  of  money  in  13 
cents? 

(4)  13  quarts  of  berries  will  fill  gallon 

buckets  and . 

(5)  I  paid  1  dime  for  a  tablet.  How  much 
change  did  I  get  from  13  cents  ? 

(6)  The  milkman  had  13  bottles  of  milk  in  his 
wagon.  He  left  4  bottles  with  us.  How  many  are 
still  in  the  wagon  ? 

(7)  The  farmer  has  13  horses.  8  horses  are  at 
work.    How  many  teams  are  idle  ? 

(8)  A  livery  man  has  13  carriages.  5  carriages 
are  out.    How  many  are  left  in  the  barn  ? 


96  Two  Years  Work  in  Ntimhers 

Exercise  38 


TEST 


13- 
13- 

1-    2  — 

r-10  — 

2x4  — 
3x    3  — 

2 
1 
4 

13- 

-    3  — 

4x    3  — 

5 

13- 

-    4  — 

3x    2  — 

6 

13  H 

-5  — 

5x    2  — 

8 

13-7  — 
13  -     3  — 

2x    6  — 
3x    4  = 

1 
3 
4 

13-4  — 

1x12  — 

2 

13-8  — 

1x10  — 

1 

13         9            . 

2x    1  = 

6 

13-6  — 

8+    2  — 

2 
5 

13  -     1  - 

9+    4  — 

4 

13  -  .13  — 

13         5 

8+    5  — 
6+    7  — 

6 
8 
3 

i  of  12  — 

i  of  10  - 

^  of  8  = 

J  of  12  — 

^  of  12  — 

i  of  6  - 

Copy  the  number  facts  on  this  page, 


Tico  Years  Work  in  Numbers  97 

Exercise  39 

The  pairs  of  the  number  14  are : 

7  8  9  10  11  12  13 
J7  _6  _5  ^  _3  _2  ^ 
14    14    14    14    14    14    14 

How  many  pairs  of  numbers  in  14  ?    Why  ? 
Use  inch  squares  to  show  each  combination. 
Also  take  14  inch  squares  and  show  the  two  subtrac- 
tion problems  for  each  addition  problem. 

7  14  14  8  14  14 

+7  -7  -7  +6  -8  -6 


14 

7 

7 

14 

6 

8 

9 

14 

14 

10 

14 

14 

+5 

-9 

-5 

+4 

-10 

-4 

14  5  9  14  4  10 

There  were  14  children  in  the  class  at  school. 

6  were  kept  at  home  with  the  measles,  how  many 

were  at  school  ?  14  -  6  :=  ? 

Write  the  pairs  of  the  number  14,  three  times. 

Exercise  40 

• 

In  1  week  how  many  days  ? 

In  2  weeks  how  many  days  ? 

In  2  weeks  how  many  school  days  ? 

2  weeks  less  10  days  are days. 

How  many  days  in  2  weeks  that  you  do  not  go  to 
school  ? 


98  Two  Years  Work  in  Numbers 

How  many  half -days  in  1  week  ? 

If  a  street  car  conductor  gets  2  dollars  a  day,  how 

many  dollars  will  he  make  in  a  week '? 
If  he  received  1  dollar  a  day,  how  long  would  it 

take  him  to  earn  14  dollars? 
In  14  days  how  many  Sundays  ?     Saturdays  ? 
If  in  2  weeks  you  spend  10  days  in  school,  how 

many  days  are  you  out  of  school  ? 
There  are  9  boys  in  the  A  class  and  5  boys  in  the 

B  class.    In  both  classes  there  are boys. 

Exercise  41 
Take  14  squares  and  place  them  in  2  equal  rows. 

One-half  of  14  is . 

One-seventh  of  14  is . 


2  X  7  =  14.  14  ^  2  =  7. 

J  of  14  = .        iof  14  =  — 


In  14  days  there  are weeks. 

In  14  pints  there  are quarts. 

In  14  quarts  there  are gallons  and  - 

In  14  inches  there  are  foot  and  — 

In  14  cents  there  are  dime  and 

In     7  pounds  there  are half-pounds. 

In  14  lemons  there  are dozen  and  — 

In  14  months  there  are year  and 

In  14  pecks  there  are bushels  and  — 

In  14  dimes  there  are dollar  and 


Write  tables  of  7  as  above,  three  times  each. 


Two  Years  Work  in  X umbers  99 

Exercise  42 

TEST 

14-  2-2-2-2-2-2  = 
14-  3-4  +  3  +  4-3-3  = 
14-  7  +  6  +  2-2-5-2  = 
14-10  +  4  +  2  +  1-3-5  = 


2x   2x2x2x2x2x2— 

3x   3  +  1  +  2  +  2  — 

Add    2    to 

6,    8,    3,    9,    4,  10,    7,    5. 

Add    3    to 

5,    2,    8,    6,    3,    9,  11,  10. 

Add    5    to 

5,    3,     1,    8,    6,    2,    7,    9. 

Subtract  3 

from       8,  9,  6,  5,  10,  14,     7, 

13. 

Subtract  5 

from    10,  5,  7,  6,    9,  12,  13, 

14. 

Divide  10  by  2 ;  12  by  3 ;  14  by  7 ;  9  by  3. 
Multiply    2    by    2,     6,    7,     3,     5,    4. 

James  has  to  walk  2  blocks  and  then  he  can  ride  12 
blocks.    His  home  is blocks  from  school. 

Exercise  43 

(1)  In  going  home,  Charles  rode  9  miles  on  the 
train  and  5  miles  in  the  buggy.  To  reach  his  home 
how  many  miles  did  he  travel  ? 

(2)  Charles  lives  8  blocks  North  of  the  college 
and  Walter  lives  6  blocks  South.  How  far  apart  do 
the  bovs  live  ? 

(3)  Elizabeth  lives  14  blocks  South  of  the  col- 
lege ;  James  lives  3  blocks  South.  How  far  apart 
do  Elizabeth  and  James  live  ? 


100  Two  Years  Work-  in  Numbers 

(4)  Gillette  has  2  chicken  coops  with  7  chickens 
in  each.    How  many  chickens  has  he  ? 

(5)  There  are  14  trees  to  be  planted  in  two 
equal  rows  in  front  of  the  lawn.  How  many  trees 
in  each  row  ? 

(6)  Jane  bought  8  cents  worth  of  ribbon.  How 
much  change  will  she  get  if  she  hands  the  clerk  a 
dime? 

(7)  How  much  will  7  two-cent  stamps  cost? 

Exercise  44 

TEST 

2x2=  4---2=  4-v-2  = 

3x2=  6^3=  6h-2== 

6x2=  32^6=  12-4-2  = 

3x3=  9-^3=  9-T-3  = 

4x3=  12 -^4=  12 -=-3  = 

5x1=  5--5=  5--l  = 

3x1=  3-f-3=  3^1  = 

2x7=  14-^•2=  14h-7  = 

Write  the  pairs  of    7  from  memory. 

Write  the  pairs  of    9  from  memory. 

Write  the  pairs  of  14  from  memory. 

In  two  weeks  there  are working  days. 

How  many  eyes  have  7  birds  ? 

Think  of  a  word  having  7  letters. 

How  many  letters  in  the  word  Wednesday? 

How  many  letters  less  in  the  word  Sunday  ? 
2x6  +  2=?  3x3+?  =  14 

2x7-3=?  4x3+?  =  14 


Two  Years  Work  in  Numbers  101 

Exercise  45 

•  •  •  •  • 

15      •  •  •  •  •15 

•  •  •  •  • 

Count  by  3's  and  5's  to  15. 

The  number  15  is  1  ten  and  5  units. 

The  number  15  is  more  than  14. 

The  number  15  is  more  than  10. 

The  number  15  is  more  than     9. 

The  number  15  is  more  than     6. 

The  number  15  is  more  than  11. 

The  number  15  is  more  than  12. 

The  number  15  is  more  than     8. 

The  combinations  that  make  the  number  15  are : 

7  9        10        11         12        13         14 

_8        _6        _5        J        _3        J        _1 
15        15        15        15        15        15        15 

Copy  each  of  the  above  combinations  four  times. 

Exercise  46 

Place  15  inch  squares  in  a  row. 

My  row  is foot  and inches  long. 

(Use  ruler.) 


102  Two  Years  Work  in  Numbers 

I  can  make  a  rectangle inches  long  and 

inches  wide. 
I  find  there  are fives  in  15.       -i  of  15  is  — 


One-third  of  15  is . 

Two-thirds  of  15  are  ■ .  -|  of  15  are 

Three-thirds  of  15  are . 

I  find  there  are threes  in  15.    -g  of  15  is  — 

One-fifth  of  15  is . 

Two-fifths  of  15  are  • .  g  of  15  are 

Three-fifths  of  15  are . 

Four-fifths  of  15  are .  g  of  15  are 

Five-fifths  of  15  are . 


Show  with  the  squares  that  you  take  five  3  times 

to  make  15. 
3  times  5  are  15. 

I  take  three  5  times  to  make  15. 
5  times  3  are  15. 

Exercise  47 

Copy  and  change  each  of  the  following  addition 
problems  to  two  subtraction  problems : 


Add: 

7          8 

9 

6 

8 

9 

6 

8 

8          3 

4 

5 

6 

3^ 

1_ 

4 

8         3 

8 

6 

11 

9 

8 

9 

1         7 

5 

9 

3 

1 

2 

5 

Two  Years  Work  in  Numbers 


103 


2x6  books  are  — 
3x3  pencils  are 
2x7  boys  are  — 


I  can  buy 
I  can  buy 
I  can  buv 


3x4  boxes  are 
2x5  cents  are 
3x5  cents  are - 


tablets  for  15  cents, 
pencils  for  15  cents, 
oranges  for  15  cents. 


Write  the  odd  numbers  to  100. 


Exercise  48 

There  are  30  days  in  June. 
In  one-half  of  the  month  of  June  there  are 
days. 

15  days  are weeks  and day. 

15  feet  are yards. 

15  pints  are quarts  and pint. 

15  months  are year  and months. 

15  things  are dozen  and things. 

15  dimes  are dollar  and dimes. 


15  cents  are  — 

15  inches  are 

15  school  days  are 
15  cents  will  buy  - 


dime  and  - 
-  foot  and 


cents. 
-  inches. 


school  weeks. 
and 


What  two  pieces  of  money  make  15  cents. 
One-half  foot  and  what  number  of  inches  make  15 

inches  ? 
How  many  squares  can  you  make  out  of  15  inch 

squares?    How  many  will  you  have  left? 


104  Two  Years  Work  in  Numbers 

Exercise  49 

TEST  QUESTIONS 

How  many  points  have  5  triangles  ? 
How  many  feet  have  3  cows  ? 
How  many  gloves  will  7  ladies  wear  ? 
How  many  shoes  will  10  ladies  wear? 
How  many  yards  will  12  feet  make  ? 
How  many  quart  jars  will  2  gallons  fill? 
How  many  pint  bottles  will  7  quarts  fill  ? 
How  many  fingers  and  thumbs  on  3  hands 
How  many  cents  in  3  nickels? 
How  many  cents  in  a  dime  and  a  nickel  ? 
How  many  pint  cups  will  12  gills  fill  ? 
How  many  feet  will  5  yards  make  ? 
How  many  points  have 3 stars? 
How  many  stripes  has  our  fiag? 
How  many  half-dozens  in  15  eggs  ? 
How  many  threes  in  15  ? 

Write  each  of  these  words  5  times : 


Exercise  50 

In  the  following,  change  each  combination  of  the 
number  15  to  two  subtraction  problems. 


Two  Years  Work  in  Numbers  105 


Add: 

7 

9 

5 

4 

3 

2 

1 

■8 

6 

10 

11 

12 

13 

14 

In  the  following,  change  the  multiplication  facts 
to  two  division  facts : 

2x6  = .  12  ^  2  =  i  12  ^  6  =  ? 

3x4  = .  12  H-  3  =  ?  12  -4-  4  =  ? 

7x2  = .  14  H-  7  =  ?  14  H-  2  =  ? 

3x5  = .  15  ^  3  =  ?  15  ^  5  =  ? 

We  can  write  division  problems  four  ways : 

(1). 
12  divided  bv  3  are  4.  (3)  (4) 


(2) 
12      -^      3     =    4 


3)12  12 

- —  —  ^=  4. 


4  3 

3)  9        5)10        2)10        2)13        7)14 


3)15        4)15        5)15        6)15        7)^15 

Exercise  51 

(1)  The  boj'  had  15  apples  in  his  basket.     He 
sold  1  dozen.    How  many  had  he  left  ? 

(2)  There  were  9  roses  on  1  bush  and  6  roses  on 
the  other.    On  both  bushes  there  were roses. 

(3)  Lucy  and  Mary  each  bought  a  half-dozen 
oggs.    They  both  bought fggs  or do^en. 


106  Two  Years  Work  in  Numbers 

(4)  Lucy  used  8  yards  for  her  skirt  and  3  yards 
for  her  waist.    She  used yards  for  her  dress. 

(5)  The  trimmer  used  5  yards  of  ribbon  on  each 
hat.    3  hats  required yards. 

(6)  Beatrice  bought  6  yards  of  lace  for  one 

dress  and  4  yards  for  another.  Beatrice  used 

yards  on  both  dresses. 

(7)  Raisins  are  15  cents  a  pound.    J  of  a  pound 
costs cents. 

(8)  8  boys  and  7  girls  were  studying  arithmetic. 
children  were  studying  arithmetic. 

Exercise  52 

ORAL 

Add  2  to  3,  8,     5,     7,     6,  4,  9. 
Add  5  to  2,  9,     8,.  3,  10,  7,  6. 
Add  6  to  7,  1,     8,     9,     3,  5,  3. 
Add  4  to  9,  7,  10,  11,    3,  8,  4. 
Multiply  3,   7,  5,  4,   6,   2  by  2 
Divide  14,  12,  10,  8,  6,     4,  by  2. 
Divide  15,  12,    9,  6,  3,  10,  by  3. 
Count  backwards  from  99  by  10 's. 
Count  backwards  from  97  by  10 's. 

WRITTEN  WORK 

Take  the  following  combinations  to  100 1 

12-8  =  4.  13-7  =  6. 

12-5  =  7.  13-9  =  4, 

7  +  8  =  15.  9  +  6  =  15. 


Two  Years  Work  in  Numbers  107 

Exercise  53 


We  have  reached  another  square  in  our  numbers. 

What  is  it  the  square  of  ? 
How  many  inch  squares  will  it  take  to  make  this 

square  ? 
How  many  inches  will  my  pencil  travel  in  going 

around  this  square  ? 
Name  the  other  squares  we  have  studied. 


108  Two  Years  Work  in  Numbers 

Exercise  54 

Take  16  inch  squares  and  make  a  4-inch  square. 

How  many  4  's  in  16  ?    One-fourth  of  16  is 

Two-fourths  of  16  are . 

Three- fourths  of  16  are . 


Take  the  16  inch  squares  and  make  a  rectangle. 

How  long  is  the  rectangle  ?    How  wide  ? 

How  many  inches  will  the  pencil  travel  in  going 

around  this  rectangle  ? 
What  is  one-half  of  16  inch  squares  ? 
Waht  are  two-halves  of  16  inch  squares? 
What  is  one-eighth  of  16  inch  squares? 
What  are  two-eighths  of  16  inch  squares  ? 
What  are  three-eighths  of  16  inch  squares  ? 
What  are  four-eighths  of  16  inch  squares  ? 
What  are  five-eighths  of  16  inch  squares  ? 
What  are  six-eighths  of  16  inch  squares? 
What  are  seven-eighths  of  16  inch  squares  ? 
What  are  eight-eighths  of  16  inch  squares. 

Exercise  55 
The  pairs  of  numbers  that  make  16  are : 
8        9       10       11       12      13       14      15 

16       16       16       16       16      16      16      16 

Commit  the  above  to  memory. 

4  times  4  are .  16  divided  by  4  are . 

2  times  8  are .  16  divided  bv  8  are . 


Tico  Years  Work  in  Xiaithcrs  109 


i  af  16  is  .  i  of  16  is 


I  of  16  is  .  I  of  16  are  . 

(1)  Frank  is  9  years  old.  How  many  years 
must  he  live  to  be  16  years  old? 

(2)  The  baker  sent  8  loaves  of  bread  to  each  of 
two  stores.    How  many  loaves  did  he  sell  ? 

(3)  Mother  has  16  pieces  of  candy.     She  wants 

to  divide  them  equally  among  her  two  daughters 

and  two  sons.     How  many  pieces  will  each  child 

get? 

Exercise  56 

Write  pairs  of  16  from  memory  and  change  each 
addition  fact  to  two  subtraction  facts,  as : 

9  16  16 

+7-9-7 

(1)  There  were  16  boys  and  7  girls  on  the  car. 
How  many  more  boys  than  girls  ? 

(2)  Measure  a  4  foot  square  table.  How  many 
square  feet  of  oil  cloth  will  it  take  to  cover  the  top 
of  it? 

(3)  If  you  want  the  above  cover  to  fall  2  inches 
over  each  edge,  how  much  oil  cloth  must  you  buy  ? 

(4)  Mrs.  A.  bought  2  pecks  of  cherries.  How 
many  quarts  did  she  get  ? 

(5)  16  pints  of  jelly  are quarts  of  jelly. 

(6)  Mary's  doll  house  is  4  feet  square.  If  she 
could  buy  carpet  1  foot  wide,  how  many  square  feet 
of  carpet  would  it  take  to  cover  the  floor?  How 
many  yards  1  foot  wide  ? 


110             2'wo  Years  Work  in  S utnbers 

Exercise  57 

11+?  =  15  ?  +  4=5  2x4=    ? 

3+?  =  16  ?  +  3=8  2x5=    % 

8+?  =  16  '?  +  2=9  6x2=    % 

4  +  ?  =  10  ?  +  6  =  11  ?  X  4  =  12 
3+?  =  13  ?  +  7  =  12  ?x3=  9 
4+?  =  13  ?  +  4  =  13  ?  +  2=8 
5+?==  14  ?  +  3  =  14  ?x5  =  15 
6+?  =  13  1  +  2  =  11  4x4=  ? 
7+?  =  12  .  ?  +  7  =  13  3x?  =  12 
8+?  =  14  ?  +  8  =  15  ?x6  =  12 
9+?  =  15  ?  +  9  =  16  5x1  =  15 
6+?  =  12  1  +  6  =  15  4x1  =  12 

7  +  8=1  12 -1  =  7  16 -+-4=1 

8  +  5=1  13 -1  =  5  16-H-1  =  8 

5  +  6=1  14-7=1  12-=-3=1 

6  +  3=1  13-8=1  10-^-1  =  2 

9  +  2=1  15-9=1  9-f-3=1 
10 +  5=1  16 -5=1  12 -7-2=1 


Two  Years  Work  in  Numbers  111 

Exercise  58 

16  ounces  make  a  pound. 

We  buy by  the 

pound. 
If  candy  is  20  cents  a  pound,  8  ounces  will  cost 

cents. 
If  beef  is  10  cents  a  pound,  one-half  pound  is  worth 

cents. 

If  flour  is  5  cents  a  pound,  one-half  pound  costs 

cents. 

If  cheese  is  20  cents  a  pound,  one-fourth  of  a  pound 

costs cents. 

At  40  cents  a  pound,  4  ounces  of  candy  costs 

dime. 
At  32  cents  a  pound,  8  ounces  will  cost  — —  cents. 

One-half  of  a  pound  is ounces. 

One-fourth  of  a  pound  is ounces. 

Two-fourths  of  a  pound  are ounces. 

Three-fourths  of  a  pound  are ounces. 

Exercise  59 

Use  inch  squares  and  work  out  the  pairs  of  num- 
bers that  make  17. 

9765        4        321 
8      10      11       12      13      14      15      16 


112  Two  Years  Work  in  Xainbers 

In  working  out  these  combinations  see  how  many 
familiar  combinations  you  have. 

How  many  new  combinations  ? 

How  many  have  you  seen  before  ? 

Change  each  addition  combination  in  this  Exercise 
to  two  subtraction  problems. 

Is  17  an  odd  or  even  number  ?    Why  ? 

17  is  made  of  how  many  tens  and  units  ? 

16  is  made  of  how  many  tens  and  units  ? 

15  is  made  of  how  many  tens  and  units  ? 

14  is  made  of  how  many  tens  and  units  ? 

13  is  made  of  how  many  tens  and  units  ? 

12  is  made  of  how  many  tens  and  units  ? 

11  is  made  of  how  many  tens  and  units? 

Exercise  60 

(1)  There  are  10  boys  and  7  girls  in  the  class. 
How  many  children? 

(2)  Why  is  it  you  can  add  the  number  of  boys 
and  girls?    ^^ Because  we  call  them  children." 

(3)  What  must  you  call  8  books  and  9  pencils  in 
order  to  add  them  ? 

(4)  What  must  you  call  11  birds  and  6  chickens 
in  order  to  add  them  ? 


Two  Years  Work  in  Numbers  113 

(5)  What  must  you  call  13  men  and  4  women 
that  you  may  add  them  ? 

(6)  What  must  you  call  5  pigs  and  2  horses  that 
you  may  add  them  ? 

(7)  How  must  you  change  quarts  and  pints  in 
order  to  add  them  ? 

(8)  How  can  you  subtract  days  from  1  month  ? 

(9)  What  must  you  do  to  add  inches  and  feet  ? 

Exercise  61 

We  have  learned  that  we  can  add  only  things  that 
have  the  same  name. 

We  also  have  learned  that  we  can  subtract  only 
things  that  have  the  same  name. 

This  is  why  we  must  always  write  dollars  in  the 
same  column  and  cents  in  the  same  column  to 
add  or  subtract  them. 

Add  Subtract  Add 

$10.05  $20.60  $3.01 

$  1.30  $10.30  $2.10 

$  3.21  $1.15 

If  we  have  a  dollar  and  we  earn  50  cents,  we  have 
a  dollar  and  50  cents,  or  one  dollar  and  a  half. 


114  Two  Years  Work  in  Numbers 

If  we  had  a  dollar  and  a  half  and  spent  a  quartei^ 
of     dollar,  how  much  money  did  we  have  left  ^ 

Let  the  children  solve  a  number  of  similar  prob- 
lems from  the  board. 


Exercise  62 

One  dollar  is  equal  in  value  to half  dollars. 

One-half  dollar  is  equal  in  value  to quarters. 

One-half  dollar  and  one  quarter  are cents. 

Five  dimes  and  a  quarter  of  a  dollar  are cents. 

Two  dimes  and  a  nickel  are cents  or . 

Two  dimes  and  a  nickel  are  what  part  of  a  dollar  ? 
Five  nickels  are  what  part  of  a  dollar  ? 
Five  dimes  are  what  part  of  a  dollar  ? 

Copy  the  following  addition  facts,  and  change 
each  one  to  two  subtraction  problems : 


2 

7 

6 

7 

8 

9 

7 

8 

9 

8 

9 

3 

5 

6 

9 

6 

5 

8 

5 

9 

7 

9 

6 

5 

8 

9 

7 

7 

4 

8 

5 

9 

6 

3 

2 

3 

Two  Years  Work  in  yumbers  115 


Exercise  63 

9  + 

8  — 

2x5  = 

3 

4 

6  + 

5  — 

10   :   2  — 

3 

4 

8  + 

6  — 

6x2  — 

3 

4 

9  + 

7  — 

12    :   6  — 

3 

4 

10- 

5  — 

12 --2  — 

3 

4 

11- 

2  — 

3x5- 

3 

4 

13- 

9  — 

15    :   3  — 

3 

4 

10  + 

4  — 

9x1  — 

3 

4 

9  + 

6  — 

15   :    5  — 

3 

4 

12  + 

5  — 

12  -J-  4  - 

3 

4 

11  + 

6  — 

2  X  4  = 

3 

4 

14  + 

3  — 

12   :   3  — 

3 

4 

12- 

7  = 

4x4  — 

3 

4 

7  +  : 

10  — 

8   :   4  = 

3 

4 

8  + 

5  — 

16   :   8  — 

3 

4 

17- 

9  = 

3x3  = 

3 

4 

15- 

9  = 

16 --4-= 

3 

4 

11- 

9  — 

17  :   9  — 

3 

4 

lit)  Two  Years  Work  in  y umbers 

Exercise  64 
7  15  3  6  9 


+3 

Add  3  to  each  number  given  above.    Also  add  2,  4, 

5,  6,  7,  and  8  to  each  number  given  above. 
^  ame  the  pairs  of  numbers  that  make  10. 
Name  the  pairs  of  numbers  that  make  16. 
Name  the  pairs  of  numbei:s  that  make  17. 

(1)  There  are  17  dollars  in  my  pocketbook.  If  I 
pay  a  milk  bill  of  5  dollars,  how  many  dollars  have 
Heft? 

(2)  If  it  costs  8  dollars  to  travel  to  Muskogee 
from  Oklahoma  City,  what  will  it  cost  to  go  to  Mus- 
kogee and  return  ? 

(3)  If  Charles  makes  6  dollars  a  day  in  a  mill, 
what  will  he  make  in  2  days  ? 

(4)  In  17,  how  many  twos  ?  How  many  threes  % 
How  many  fours  ?  How  many  fives  ?  How  many 
sixes  ? 

Exercise  65 

18  is ten  and units. 

We  use figures  to  write  18. 

Use  inch  squares  and  show  all  the  pairs  of  numbers 
that  make  18. 

9      10      11      12      13      14      15      16      17 

9        ?        ??        ?        ?        ?        ?        ? 

How  many  pairs  in  18  things  ? 


Two  Years  Work  in  Numbers  117 

Make  a  rectangle  6  inches  long  and  inches 

wide  with  your  18  inch  squares. 

6  times  what  are  18?        J  of  18  is  . 


f  of  18  are  .  f  of  18  are  . 

i  of  18  are  .  f  of  18  are  . 

Copy  pairs  of  17, 16,  15,  14  from  memory. 
Copy  pairs  of  18  from  the  board. 

Exercise  66 

Take  18  inch  squares  and  make  a  rectangle  9  inches 
long  and inches  wide. 

How  many  2's  in  18?  How  many  9's  in  18? 

i  of  18  is  .  f  of  18  are  — 

i  of  18  is  f  of  18  are  — 

f  of  18  are  .  t  of  18  are  — 

f  of  18  are  .  f  of  18  are  — 

J  of  18  are  — — .  f  of  18  are  — 


Copy  and  solve  the  following : 

2  X  ?  are  18.  3  x  ?  are  18. 

9  X  ?  are  18.  6  x  ?  are  18. 

3x5  are .  3  +  ?  are  12. 

4  X  4  are .  2  +  ?  are  12. 

2  X  8  are .  2  +  ?  are  10. 

3  X  3  are .  2  +  ?  are  14. 

5  X  3  are  — .  3  +  ?  ai^e  15. 


118  Two  Years  Work  in  Numbers 


Exercise  67 

1  dozen  and  a  half  eggs  are eggs. 

1  foot  and  6  inches  are inches. 

1  year  and  6  months  are months. 

In  18  working  days  how  many  weeks? 

In  18  feet  how  many  yards  ? 

In  18  pints  how  many  quarts  ? 

In     1  square  yard  how  many  square  feet  ? 

In  18  pecks  how  many  bushels  ? 

In  18  inches  how  many  feet? 

In  18  gills  how  many  pints  ? 

In  18  cents  how  many  dimes? 

In  18  cents  how  many  nickels? 

In  18  days  how  many  weeks  ? 

In  18  months  how  many  years  ? 

In  18  weeks  how  many  months  ? 

Write  the  pairs  of  18  and  change  each  pair  to  two 
subtraction  problems. 


Two  Years  Work  in  Numbers  119 


Exercise  68 

How  many  2's  in  18? 

4 

5 

6 

How  many  3 'sin  18? 

4 

5 

6 

How  many  4's  in  18  ? 

4 

5 

6 

How  many  5's  in  18? 

4 

5 

6 

How  many  6  's  in  18  ? 

4 

5 

6 

How  many  7's  in  18? 

4 

5 

6 

How  many  8's  in  18? 

4 

5 

6 

How  many  9 'sin  18? 

4 

5 

6 

(1)  There  are  10  quarts  of  cherries  on  the  table 
and  8  quarts  of  berries.  How  many  quarts  of 
fruit? 

(2)  9  trees  in  one  row.  In  two  rows  there  are 
trees. 


(3)  3  half-dozen  eggs  are eggs. 

(4)  How  many  2-cent  stamps  can  be  bought  for 
18  cents? 

(5)  How  many  3-cent  stamps  can  be  bought  for 
18  cents? 

Write  numbers  to  100. 


120 


Two  Years  Work  in  Numbers 


Exercise  69 

If  necessary,  use  objects  in  solving  the  following 
problems  • 


19  is 
19  is 
19  is 
19  is 
19  is 
19  is 

18  is 

19  is 
17  is 
17  is 
15  is 
14  is 
17  is 
19  is 
19  is 
19  is 
19  is 


ten  and  - 

5  more  than 
10  more  than 
3x5  and  — 
9  more  than 
3x6  and  — 
2+7  and  — 
2  X  8  and  — 
3x5  and  — 
4x4  and  — 
3x4  and  — 
2  ^;  6  and  — 
2x7  and  — 
3x3  and  — 
5x2  and  — 
2x5  and  — 
2 


units. 


X  9  and 


2 
1 
3 
4 
5 
6 
7 


6 
2 
5 
4 
3 
4 


4 

2 
3 
7 
1 
8 
1 


8 
1 
5 
6 
4 
2 


Copy  the  following  problems : 

987654321 
10  11  12  13  14  15  16  17  18 
19     19      19      19      19     19     19     19      19 


Two  Years  Work  in 

Numbers 

Exercise  70 

TEST 

1x1  — 

3  x 

4  — 

15  :  5  = 

2x1  — 

2  X 

7  — 

9   :   3  = 

3x1  — 

7  X 

2  — 

10 -f- 3  = 

1x4  — 

3  X 

5  — 

12  :  6  = 

2x2  — 

5  X 

3  — 

12  :  2  = 

1x5  — 

4  X 

4  — 

16 -f- 4  = 

2x3  — 

2  X 

8  — 

18  :  3  = 

1x6  — 

2  X 

9  — 

8  :  9  = 

1x7  = 

3  X 

6  — 

18  :  6  = 

2x4  = 

10^ 

■2  — 

6^3  = 

1x8  = 

12-- 

3  — 

9  +  6  — 

3x3  — 

14  : 

2  — 

8  +  7  — 

1x9  = 

15  : 

3  — 

6  +  5  — 

10x1  — 

18  : 

9  — 

7  +  9  — 

11x1  — 

16  : 

2  — 

9  +  9  = 

2x6  — 

10  : 

5  — 

8  +  5  = 

12x1  — 

12  : 

4  — 

9  +  3  — 

121 


Copy  this  page  and  recite  orally. 

^  of    9  is  — — .  4  of  16  is 

^  of  15  is .  ^  of  18  is 

i  of  12  is .  i  of  18  is 

J  of  16  is  - — .  ^  of  18  is 


122  Two  Years  Work  in  Numbers 

Exercise  71 

(1)  It  requires  1  week  and days  to  make 

19  days. 

(2)  It  requires  1  year  and month  to  make 

13  months. 

(3)  It  requires  4  gallons  and quarts  to 

make  19  quarts. 

(4)  It  requires  4   gallons   and  quart  to 

make  17  quarts. 

(5)  It  requires  3  yards  and feet  to  make 

13  feet. 

(6)  Mr.  A.  lives  10  miles  east  of  St.  Louis,  and 
Mr.  B.  lives  8  miles  west.  How  far  apart  do  they 
live? 

(7)  William  lives  9  miles  from  town.  He  can 
ride  7  miles  on  the  Interurban  car.  How  far  must 
he  walk  ? 

(8)  Henry  had  18  marbles  and  he  sold  a  dozen. 
How  many  had  he  then  ? 

(9)  half-dozen  eggs  and are  19  eggs. 

Count  by  2  's  to  100  and  then  back  to  0. 
Count  hj^  10 's  to  100  and  then  back  to  0. 
Count  by    5's  to  100  and  then  back  to  0. 


Two  Years  Work  in  Numbers 


123 


Exercise  72 

We  have  learned  the  multiplication  table  to  18. 
We  shall  learn  five  more  multiplication  facts  to- 
day. 


20 


2X10: 

=  20. 

20h 

-10—    2. 

4x     5: 

=  20. 

20- 
20h 

-4—5. 
-5—4. 

3x    7- 

=  21. 

21- 

21- 

-3—7. 
-7—3. 

2x11 

=  22. 

22- 

22- 

1-11—  2. 
1-    2  —  11. 

3x    8 

=  24. 

24- 
24- 

r-      3—      8. 

=-8—3. 

I  of  21 

J  of  24  = 

i  of  20 

i  of  20  = 

i  of  20 

i  of  24  = 

2  =  10. 


^  of  21  = 

Copy  each  of  the  above  multiplication  facts  five 
times ;  each  division  fact  two  times. 

Exercise  73 

Write  the  pairs  of  10,  11, 12, 13, 14, 15, 16. 

Change  each  of  these  addition  facts  to  two  subtrac- 
tion facts. 


124  Two  Years  Work  in  Numbers 

Take  the  combination  8  +  6  =  14  to  100. 


8  +  6  — 

14. 

10-2=    8. 

18+  ?  — 

? 

20  -  2  ^  18. 

28+  ?  — 

? 

30  -  2  —  28. 

38+  ?  — 

? 

40-2  —  38. 

48+  ?  — 

? 

50  -  2  =  48. 

58+  ?  = 

% 

60-2  —  58. 

68+  ?  — 

? 

70  -  2  —  68. 

78+  ?  = 

? 

80  -  2  —  78. 

88+  ?  — 

? 

90  -  2  =  88. 

98+  ?  — 

? 

100-2  =  98. 

3  +  5  =  8; 

7  +  3  — 

10; 

6  +  7  —  13. 

Exercise  74 

Try  to  learn  five  new  multiplication  facts  to- 
day.   TJse  inch  squares  to  show  these  facts. 

4x    6  =  24.  4)2£  6)24 

2  X  12  =  24.  5)25_  5)20 

5x    5  =  25. 

«       r.       ^  3)27  9)27 

3  X    9  =  27.  ^ - — 

4x    7  =  28.  4)28  7)28 

Copy  the  above  multiplication  facts  five  times. 


Two  Yeiiin  Wo)k  in  \uinbei:s  125 

J  of  27  is .  f  of  25  are . 

i  of  28  is .  i  of  21  is  . 

f  of  27  are .  ^  of  22  is  -. 

4-  of  28  is .  T^  of  20  is  . 


i  of  25  is  .  T^  of  20  are  - 

Copy  the  above  division  facts. 

Exercise  75 

Use  inch  squares  to  show  the  following : 

I  of  24  is  .  I  of  24  is  

I  of  24  are  .  |  of  24  are  — 

f  of  24  are .  |  of  24  are  — 

J  of  18  is  .  i  of  15  is  

I  of  18  are  .  ^  of  21  is  

t  of  18  are .  f  of  21  are  — 


Multiply  7,  9,     8,     5,  10,     6,     by     2. 

Multiply  6,  4,    5,    2,    7,    9,  10    by    3. 

Add    4  to  6,    3,    2,    7,    9,  10. 

Subtract  4  from    6,    9,  10,  14,  12,    8,  13. 

Subtract  7  from  10,  12,  17,  19,  20,  15,  18. 


126  Two  Years  Work  la  X umbers 

Subtract     6     from     6,     9,  14,  16,  12,     8,  11. 
Subtract    9    from  10,  14,     9,  12,  18,  15,  13. 


Exercise  76 

(1)  At  5  cents  apiece,  what  will  5  pencils  cost? 

(2)  At  3  cents  a  yard,  what  will  8  yards  of  calico 
cost? 

(3)  At  2  cents  apiece,  what  will  a  dozen  eggs 
cost? 

(4)  I  paid  27  cents  for  3  tablets.  What  did  each 
tablet  cost? 

(5)  A  man  gave  24  dollars  for  3  hogs.  Each 
hog  cost dollars. 

(6)  Elizabeth  gave  10  cents  for  some  thread  and 
10  cents  for  shoe  strings.  She  gave  the  merchant 
25  cents.    How  much  change  did  she  receive  ? 

(  7  )  In  28  days  how  many  weeks  ? 

(  8  )  In  24  oranges  how  many  dozen  ? 

(  9  )  In  27  feet  how  many  yards  ? 

(10)  In  21  cents  how  many  dimes? 

(11)  In  24  quarts  how  many  gallons? 


Two  Years  Work  in  Numbers 


127 


Exercise  77 

Try  to  learn  five  more  multiplication  facts  to- 
day.   Copy  each  five  times. 


6x5  are  30. 
3  X  10  are  30. 
4x  8  are  32. 
3  X  11  are  33. 

5x7  are  35. 


Division 


30 
5 


6V  Q        6'^ 


30 
3 

S2 

8 

35 
5 


2x  10 

3x  7 
4x  6 
5x5 
3x    8 


2  X  12  = 

6x3  = 
5  X  4  = 
6x5  = 
7x4 


=  <? 


8  +  7  = 

9  +  7  = 

8  +  6  = 
7  +  5  = 
6  +  9  = 


3  times  8,  9,  3,  5,  7. 

4  times  1,  5,  6,  3,  4. 

5  times  2,  3,  1,  4,  5. 

6  times  3,  1,  2,  5,  4. 


One-half  of  — 
One-half  of  — 
One-third  of  - 
One-fourth  of 
One-fifth  of  — 


is  6. 
is  9. 

-  is  3. 

—  is  4. 
is  3. 


Use  the  above  for  oral  drill. 


128 


Two  Years  Work  in  Numbers 


Exercise  78 


Try  to  learn  five  more  multiplication  facts. 


6x 

6  —  36. 

4  X  10  —  40. 

3  X  12  ^  36. 

8  X    5  —  40. 

4x    9  —  36. 

Division 

facts. 

36- 

!-    6  — 

6. 

40  - 

-10—4 

36  - 

r-     9  — 

4. 

40  - 

-4  —  10 

36  - 

-    4  — 

9. 

40  - 

-8—5 

36- 

-    3  — 

12. 

40  - 

-5—8 

36  - 

-12  — 

3. 

Copy  the  multiplication  facts  given  above  5  times 
and  the  division  facts  once. 


(1)  If  Henry  worked  6  days  in  1  week,  in  6 
weeks  he  would  wprk days. 

(2)  Bessie  bought  9  post  cards  at  4  cents  each. 

She  paid cents.    How  much  change  would  she 

receive  from  4  dimes  ? 

(3)  Each  of  4  boys  paid  10  cents  for  drawing 
paper.    How  much  did  they  pay  ? 

(4)  At  5  cents  a  pound,  how  much  will  8  pounds 
of  sugar  cost  ? 


Two  Years  Work  In  Numbers  129 

Exercise  79 

TEST  IN   MULTIPLICATION  AND  DIVISION 


3x    5  — 

36   : 

4  — 

100 

32 

6x    2  — 

40  : 

8  — 

-2 

-3 

3x    6  — 

27   : 

9  — 

-2. 

-3 

7x    3  — 

30   : 

5  — 

-2 

-3 

9x    2  — 

■    25   : 

5  — 

-2 

-3 

3x    9  — 

24   : 

8  — 

-2 

-3 

3x12  — 

24   : 

3  — 

-2 

-3 

4x    6  — 

24  : 

4  = 

-2 

-3 

6x    6  — 

21   : 

7  = 

-2 

-3 

7x    5  — 

22   : 

11  — 

-2 

-3 

3x    3  — 

20   : 

2  — 

2x12  — 

36   : 

12  — 

2 

3 

3  X  12  — 

32   : 

4  — 

3 

2 

9x    3  = 

33   : 

3  — 

5 

1 

4x    4  — 

36   : 

3  — 

2 

5 

2x11  — 

40   : 

4  — 

7 

2 

3x11  — 

28    : 

7  — 

9 

1 

11  X      1  — 

16   : 

8  — 

J- 

130  Ttvo  Years  Work  in  Numbers 

Exercise  80 

You  will  now  learn  7  new  multiplication  facts. 
Copy  each  of  these  facts  5  times  and  memorize 
them.  Change  each  of  these  new  multiplica- 
tion facts  to  two  division  facts,  and  copy  in 
your  tablet. 

7x    6  =  42.  6 X    8  =  48. 

4x11  =  44.  7x    7  =  49. 

9x    5  =  45.  5x10  =  50. 
4x12=48. 

5)36  3)36  2)44  2)42  4)40  11)44 

6)48  5)50  4)48  4)36  9)37  6)38 

6)40  6)42  6)25  3)27  7)27  7;^ 

5)31  8)32  10)33  6)26  8)44  8)34 


Note  :  There  should  be  frequent  drills  on  simi- 
lar division  problems.  This  is  the  best  preparation 
for  short  division. 


4  5 

1  2 
3  1 

2  3 


Two  Years  Work  hi  Numbers  131 

Exercise  81 

In  12  feet  how  many  yards  ?  12 

In  20  quarts  how  many  gallons  ?         2  2 

In  24  quarts  how  many  pecks  ?  3  2 

In  40  pecks  how  many  bushels  ? 

In  50  cents  how  many  dimes? 

In  30  cents  how  many  nickels? 

In  48  gills  how  many  pints  ? 

In  48  pints  how  many  quarts  ?  4  ^ 

In  36  feet  how  many  yards  ?  3  5 

In  36  inches  how  many  feet? 

In  48  inches  how  many  feet?  2  4 

In  28  days  how  many  weeks?  3  8 

In  12  weeks  how  many  months  ?  1  3 

In  48  months  how  many  years  ?  3  2 

In  25  school  days  how  many  school       ^  ^ 

weeks?  ^  _3 

Copy  the  following  5  times : 

7x    6  =  42.  3x12  =  36. 

8x    6  =  48.  7x    7  =  49. 

3x    9  =  27.  4x    9  =  36. 

8x  4  =  32. 


132 


Two  Years  Work  in  Numbers 


Exercise  82 

ADDITION    SQUARE 


Z 

I 

4 

7 

5 

3 

9 

6 

8 

5 

7 

6 

9 

1 

3 

2 

5 

7 

3 

2 

6 

9 

8 

4 

Note  : — Add  each  number  in  the  squares  of  the 
left  column  to  each  number  in  the  squares  of  the 
top  row.  Place  the  sum  in  the  square  below  the 
number  of  the  top  row  and  to  the  right  of  the  num- 
ber of  the  left  column,  as  shown  in  the  cut.  Use 
the  same  plan  for  subtraction,  multiplication  and 
division. 


Two  Years  Work  in  Numbers  133 

Exercise  83 


Add 


4   9   3  10   94   6   9   5   7 
3   263254557 

L     1^     ^     ^      :^iL^i_^± 

(1)  A  farmer  has  10  cows,  7  horses  and  5  sheep. 
He  has animals. 

(2)  Anna  has  7  dollars,  Mary  has  6  dollars  and 
eTohn  has  10  dollars.    How  many  dollars  have  all  ? 

(3)  James  came  to  school  5  days  in  one  week;  3 
the  next,  4  the  next  and  5  the  next.  How  many 
days  did  he  attend  school  that  month  ? 

(4)  I  gave  5  cents  to  one  girl,  7  to  another,  10 
to  another.    To  all  I  gave cents. 

(5)  If,  during  the  week,  I  paid  10  dollars  for 
groceries,  4  dollars  for  coal,  2  dollars  for  lights, 
and  25  cents  for  water,  how  much  were  my  house 
expenses  that  week  ? 

(6)  A  lady  had  4  chairs  in  one  room,  6  in  an- 
other and  5  in  another.    How  many  in  all  ? 


dd: 

Exercise  84 

20 

22 

33          24          25 

35 

66 

10 

10 

10          10          10 

10 

10 

134  Two  Years  Work  in  Numbers 


20 

22 

33 

24 

25 

35 

66 

11 

11 

n 

11 

11 

11 

11 

20 

22 

33 

24 

25 

35 

66 

12 

12 

12" 

12 

12 

12  " 

12 

20 

22 

33 

24 

25 

35 

66 

20 

20 

20 

20 

20 

20 

20 

Adding  by  10  is  the  same  as  counting  by  10. 
Adding  by  11  is  the  same  as  counting  by  10  and 

adding  1. 
Adding  by  12  is  the  same  as  counting  by  10  and 

adding  2. 
Adding  by  20  is  the  same  as  counting  by  10  twice. 
Adding  by  40  is  the  same  as  counting  by  10  four 

times. 


Exercise  85 


Subtract : 


12 

17 

15 

17 

13 

14 

13 

16 

17 

2 

9 

8 

8 

7 

8 

9 

_8 

6 

10 

12 

6 

9 

11 

13 

16 

18 

15 

3 

7 

3 

5 

9 

5 

9 

9 

5 

(1)  18  pupils  belonged  to  the  school.    6  pupils 
were  absent.    How  many  were  present? 


Two  Years  Work  in  Numbers  135 

(2)  A  man  raised  20  bushels  of  potatoes,  and 
sold  5  bushels.    He  kept bushels. 

(3)  Mr.  A.  bought  a  calf  for  10  dollars  and  sold 
it  for  18  dollars.  Did  he  make  any  money?  If  so, 
how  much  ? 

(4)  Fred  bought  2  dozen  oranges  and  sold  one 
dozen.    How  many  oranges  had  he  left  ? 

(5)  Mr.  B.  planted  19  trees.    8  trees  died.    

trees  lived. 

(6)  Lucy  had  25  cents.  She  gave  10  cents  for  a 
yard  of  lace.  What  pieces  of  money  would  she  get 
in  change  ? 


Subtraction 

Exercise  86 

1 

43 
10 

62 
10 

82 
10 

45 
10 

25 
10 

34 
10 

64 
10 

53 
11 

42 
11 

82 

n 

66 
11 

45 
11 

64 
11 

34 
11 

44 
"  12 

33 
12 

68 
12 

55 
12 

49 
12 

48 
12 

45 
12 

44 

20 

48 
20 

52 
20 

65 
20 

77 
20 

80 
20 

60 
20 

136  Two  Years  Work  in  Numbers 

Subtracting  10  is  the  same  as  eoimting  backwards 
by  10. 

Subtracting  11  is  the  same  as  counting  backwards 
by  10  and  then  taking  away  1. 

Subtracting  20  is  the  same  as  counting  backwards 
by  10  two  times. 


Exercise  87 

Multiply: 

5   9  12  11  10   7   6   8   7 
7^3457645 


365   12   34539 
742244583 


(1)  If  a  street  car  runs  6  miles  in  1  hour,  in  5 
hours  it  will  run miles. 

(2)  What  is  the  cost  of  10  pounds  of  sugar  at  5 
cents  a  pound? 

(3)  What  will  7  trees  cost  at  one-half  dollar 
apiece  ? 

(4)  10  yards  of  ribbon  at  5  cents  a  yard,  costs 
cents. 

(5)  4  horses  at  $100.00  apiece  will  cost dol- 
lars. 


Two  Years  Work  in  Numbers  137 

(6)  If  a  boy  gathers  2  quarts  of  berries  in  1 
hour,  in  7  hours  he  can  gather quarts  of  ber- 
ries. 

(7)  At  3  cents  a  yard,  12  yards  of  lace  will  cost 
cents. 

Exercise  88 

Divide : 

3)12       10)50       3)33       7)42       4)32       3)27 


2)14         7)21       3)24       4)28       4)36       7)35 

(1)  If  7  pencils  cost  35  cents,  1  pencil  will  cost 
—  cents. 


(2)  If  9  yards  cost  45  cents,  1  yard  will  cost 

cents. 

(3)  If  9  bins  hold  36  bushels,  1  bin  will  hold  — — 
bushels. 

(4)  Mary  has  $1.00.  How  many  things  can  she 
get  if  each  one  costs  10  cents  ? 

(5)  How  many  pounds  of  sugar  at  5  cents  a 
pound  can  you  buy  for  10  dozen  of  eggs  at  10  cents 
a  dozen  ? 

(6)  How  many  yards  of  calico  at  8  cents  a  yard, 
can  you  buy  for  4  dozen  eggs  at  12  cents  a  dozen  ? 

(7)  At  6  dollars  a  week,  how  long  will  it  take  a 
boy  to  earn  36  dollars  ? 


138  Two  Years  Work  in  Numbers 

Exercise  89 
Add: 

9857999753 

Subtract : 
10     17     13     16     11     12     13     15     16     12 

Multiply: 
12       7     11       6       8       9       4       9       6       5 

Divide : 

18  by  9;  27  by  3;  34  by  6;  21  by  7;  28  by  4; 
24  by  3;  24  by  12;  15  by  5;  18  by  2;  16  by  4. 

Let  pupils  make  concrete  problems,  using  the 
above  combinations. 

Count  by6'stol00. 

Count  backwards  from  100  to  0  by  5's. 

Count  to  100  by  3 's. 

Count  to  100  by  4's  and  then  back  to  0. 


Two  Years  Work  in  Numbers  139 


Exercise  90 

Make  a  clock  face  and  learn  to  tell  the  time  from  it. 

Use  your  circle-maker  and  draw  an  eight-inch 
circle. 

Draw  a  six-inch  circle  inside. 

Divide  your  circle  into  halves  and  quarters. 

What  letters  will  you  place  at  the  top? 

What  letters  will  you  place  at  the  bottom? 

What  letters  midway  to  the  right? 

What  letters  midway  to  the  left? 

Into  how  many  equal  parts  must  each  quarter  be 
divided  to  show  all  the  hours  on  the  face  of  the 
clock? 

Now  draw  a  two-inch  circle  in  the  center. 

Place  the  short  hand  past  I  and  the  long  hand  at 
VI.    What  time  is  it? 

Imagine  the  long  hand  at  IX.    What  time  is  it  ? 

How  many  minutes  between  the  numbers  on  the 
face  of  the  clock  ? 

5  X  ?  =  10.  5  X  ?  =  30. 

12  X  ?  =  60.  5  X  ?  =  15. 


140  Ttvo  Years  Work  in  Numbers 

Exercise  91 


TEST 


6  X  ?  —  30. 

30  :  f  — 6. 

7  + 

8—  ? 

7  X  ?  —  14 

14  :  7  —  ? 

8  + 

6—  ? 

8  X  ?  —  32 

32  --  ?  —  8 

9  + 

2—  ? 

9  X  ?  —  36 

36  :  ?  — 9 

8  + 

5—  ? 

7  X  ?  —  35 

35  :  7  —  ? 

7  + 

4—  ? 

8  X  ?  —  40 

40  :  ?  — 8 

9  + 

5=  ? 

5  X  ?  —  45 

45  --  ?  —  5 

7  + 

7—  ? 

6  X  ?  —  42 

42  -^  ?  —  6 

6  + 

5=  ? 

8  X  ?  —  48 

48  :  6  —  ? 

6  + 

9—  ? 

7  X  ?  —  49 

49  :  7  —  ? 

8  + 

2—  ? 

5  X  ?  —  30 

50  :  5  —  ? 

7  + 

8—  ? 

5  X  ?  —  40 

40  :  8  —  ? 

2  + 

6—  ? 

3  X  ?  —  21 

21  :  3  =  ? 

1  + 

8=  ? 

9  X  ?  —  27 

27  :  9  =  "? 

3  +  : 

10—  ? 

8  X  ?  —  24 

24  :  8  —  ? 

2  + 

9—  ? 

6  X  ?  —  24 

24  :  6  —  ?  • 

7  + 

9   ? 

3  X  ?  —  30 

30  :  3  —  ? 

6  + 

4—  ? 

4  X  ?  —  b6 

36  --  4  —  ? 

6  + 

7—  ? 

Copy  the  above  facts. 


Two  Years.  M^ork  in  Niunbtrs  141 


Exercise  92 

(1)  Image  an  oblong  2  inches  wide  and  5  inches 
long.    How  many  square  inches'^ 

(2)  Image  a  square  5  inches  by  5  inches.    How 
many  square  inches  ? 

(3)  Image  a  square  3  feet  by  3  feet.    How  many 
square  feet? 

(4)  Image  an  oblong  3  inches  by  4  inches.    How 
many  square  inches  ? 

(5)  How  many  more  square  inches  in  the  fourth 
oblong  than  in  the  first  oblong  ? 

Note:     If  you  cannot  image  the  oblongs,  make 
them  with  inch  squares. 

(6)  Add  7  to  itself.    Add  8  to  itself.    Add  9  to 
itself.    Add  10  to  itself . 

(7)  Double  2,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15. 

(8)  Find  J  of  6,  8, 14, 18,  20,  22,  24,  26,  28,  30,  32, 
34,  36. 

(9)  Find  I  of  3,  6, 12,  9, 18,  21, 15,  24,  27,  30. 


i42  Two  Years  Work  in  Numhers 

Exercise  93 
The  45  combinations  of  Addition  are : 


1    2 

3 

2 

4 

3 

3   4 

5 

1    1 

1 

2 

1 

2 

3   2 

1 

2    3 

4 

4 

5 

5 

6   6 

6 

3  5  6 

4 

5  6 

7 

5  6  7 

8 

4  2  1 

7  7  7 

4 

8 

3  2 
8  8 

1 

8 

4  3  2 
9  9  9 

1 
9 

5  6  7  8 

9 

6  7 

8 

9 

6  7  8 

9 

5  4  3  2 

1 

5  4 

3 

2 

6  5  4 

3 

10  10  10  10  10 

11  11 

11 

11 

12  12  12 

12 

8   7   9 

7 

8 

9 

7 

9 

5   6   4 
13  13  13 

7 
14 

6 
14 

5 
14 

8 
15 

6 
15 

8 

9 

9 

9 

8 
16 

7 
16 

8 
17 

9 

18 

Here  is  a  happy  message  to  the  children :  Learn 
the  above  combinations  perfectly,  and  you  will  have 
no  trouble  with  addition  or  subtraction. 


Two  Years  Work  in  Numbers  143 

Exercise  94 


MEASURES  USED  IN  THIS  BOOK 


We  count by  this  table : 

10  ct.  10  cents  make  1  dime.  1  d. 

10  d.  10  dimes  make  1  dollar.  $1. 


We  measure by  this  table : 

12  in.  12  inches  make  1  foot.  1  ft. 

3  ft.  3  feet  make  1  yard.  1  yd. 

We  measure , , ,  by  this  table : 

144  sq.  in.      144  sq.  in.  make  1  sq.  ft.  1  sq.  ft. 

9  sq.  ft.          9  sq.  ft.    make  1  sq.  yd.        1  sq.  yd. 

We  measure , , , ,  by  this  table : 

4  gi.  4  gills  make  1  pint.  1  pt. 

2  pt.  2  pints  make  1  quart.  1  qt. 

4  qt.  4  quarts  make  1  gallon.  1  gal. 

We  measure , , , ,  by  this  table : 

8  qt.  8  quarts  make  1  peck.  1  pk. 

4  pk.  4  pecks  make  1  bushel.  1  bu. 


144  Two  Years  Work  in  Nu^nbers 

Exercise  95 
We  measure by  this  table : 

60  sec.  60  seconds  make  1  minute.  1  min. 

60  min.  60  minutes  make  1  hour.  1  hr. 

24  hr.  24  hours  make  1  day.  1  da. 

7  da.  7  days  make  1  week.  1  wk. 

4  wk.  4  weeks  make  1  month.  1  mo. 

12  mo.  12  months  make  1  year.  1  yr. 

We  measure by  this 

table : 

16  oz.  16  ounces  make  1  pound.        •       1  lb. 

The  following  is  a  test  on  the  drawings  used  in  the 
book : 

A  line  has . 


A  book  or  cube  has , and . 

A  square  has corners  and sides. 

A  star  has points. 

A  triangle  has sides  and corners. 

A  rectangle  has sides  and corners. 


Two  Years  Work  in  Numbers  145 

Exercise  96 

COMPLETION    OF    MULTIPLICATION   TABLE 

Note  to  the  Teacher  : — 

Continue  the  multiplication  table  as  far  as  you 


deem  it  wise. 

•       Pin 

om 

50  to  144. 

5  X  10  —  50. 

8x10—   80. 

6x    9  —  54. 

9x    9=   81. 

11  X    5  —  55. 

7x12—   84. 

8x    7  —  56. 

11 X    8—   88. 

6  X  10  —  60. 

9x10—   90. 

5  X  12  —  60. 

8x12—   96. 

7x    9  — 63. 

llx    9—    99. 

8x    8  —  64. 

10  X  10  —  100. 

6  X  11  =  66. 

12  x   9  =  108. 

7  X  10  =  70. 

11 X  10  — 110. 

8x   9  —  72. 

12  X 10  — 120. 

6  X  12  —  72. 

11 X  11  — 121. 

7  X  11  —  77. 

11  X  12  — 132. 

12  X 

12 

=  144. 

146  Two  Years  Work  in  Numbers 


Exercise  97 

1 

One 

I 

2 

Two 

IT 

3 

Three 

III 

4 

Four 

IV 

5 

Five 

V 

6 

Six 

VI 

7 

Seven 

VII 

8 

Eight 

VIII 

9 

Nine 

IX 

10 

Ten 

X 

11 

Eleven 

XI 

12 

Twelve 

XII 

13 

Thirteen 

XIIT 

14 

Fourteen 

XIV 

15 

Fifteen 

XV 

16 

Sixteen 

XVI 

Two  Years  Work  in  Numbers 


147 


17 

Seventeen 

XVII 

18 

Eighteen 

XVIII 

19 

Nineteen 

XIX 

20 

Twenty 

XX 

21 

Twenty-one 

XXI 

22 

Twenty-two 

XXII 

23 

Twenty-three 

XXIII 

24 

Twenty-four 

XXIV 

30 

Thirty 

XXX 

40 

Forty 

XT, 

50 

Fifty 

L 

60 

Sixty 

LX 

70 

Seventy 

LXX 

80 

Eighty 

LXXX 

90 

Ninety 

XC 

100 

One  hundred 

c 

500 

Five  hundred 

D 

1000 

One  thousand 

M 

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